%PDF-1.1 % 34 0 obj << /Length 4153 >> stream BT /F1 1 Tf 24 0 0 24 122.37 545.61 Tm 0 g BX /GS1 gs EX 0 Tc 0 Tw [(Evolution Through Imit)28(ation in a)]TJ 3.25 -2.3 TD 0.002 Tw (Single Population)Tj 15.48 0 0 15.48 403.05 501.93 Tm 0 Tw (1)Tj /F2 1 Tf 14.04 0 0 14.04 169.29 418.65 Tm 0.001 Tc 0.003 Tw [(Dav)14(id K. Lev)14(ine and )8(Wol)9(f)-3(gang)10( Pe)10(sendo)10(rfer)]TJ 9 0 0 9 437.85 425.13 Tm 0 Tc 0 Tw (2)Tj 12 0 0 12 215.61 398.61 Tm 0.003 Tc -0.001 Tw [(Fi)5(r)6(s)3(t v)13(e)-1(r)6(s)3(i)5(on: Sept)11(em)6(ber)6( 2)9(9)-1(, 1)9(9)-1(9)9(9)]TJ 1.53 -1.66 TD 0.004 Tc -0.002 Tw [(Thi)6(s)4( v)14(e)0(r)7(s)4(i)6(on: M)7(a)0(y)14( 10)10(, 2)10(000)]TJ 12 0 2.551 12 90.09 328.65 Tm 0.001 Tc (Abstract)Tj 12 0 0 12 134.25 328.65 Tm 0.004 Tc 0.338 Tw [(:)12( Ka)10(ndor)7(i)6(,)2( M)7(a)0(i)6(l)6(a)10(th )10(and)10( R)6(ob [)12(1)0(9)10(93] )10(and)10( Y)11(oung)10( [1)10(99)10(3] )-10(sh)10(ow)16(ed )-10(how)]TJ -3.68 -1.16 TD 0.068 Tw [(i)6(n)0(tr)7(oduci)6(n)0(g)10( r)7(a)0(n)10(d)0(o)10(m)-3( i)6(n)10(nov)14(ati)6(ons i)16(n)0(to )10(a )10(mod)10(e)0(l)6( of )10(ev)14(ol)6(uti)6(o)0(n)10(a)0(r)7(y)14( adj)6(ustme)10(n)0(t)12( en)10(abl)6(es)]TJ 0 -1.15 TD 0.001 Tc 0.261 Tw [(selection)7( a)7(m)-6(ong)7( Nash)7( eq)7(uilibria. K)8(e)-3(y)11( to this res)11(u)-3(lt is th)7(at )10(poorly)11( )-10(per)14(f)-11(o)-3(rm)-6(i)13(n)-3(g)]TJ T* 0.003 Tc 0.179 Tw [(str)6(a)-1(teg)9(i)5(es m)6(a)-1(y)13( be i)5(n)-1(tr)6(od)9(uce)9(d)-1( i)5(n)-1( s)13(u)9(ff)-9(i)5(c)3(i)5(e)9(nt n)9(u)-1(mb)9(er)6(s )-10(t)11(hat)11( )-10(th)9(ey)13( )-10(beg)9(i)5(n)-1( )-10(to )-10(p)9(e)-1(r)16(f)-9(or)6(m)]TJ T* 0.004 Tc 0.218 Tw [(w)16(e)0(l)6(l)6(.)2( )20(W)-32(e)0( )10(ex)14(ami)6(n)0(e)10( i)6(m)-3(i)6(t)2(ati)16(on )10(as a)10(n)0( )-10(al)6(t)12(e)0(r)7(nati)6(v)14(e )-10(an)10(d mor)7(e)0( pl)6(ausi)16(b)0(l)6(e)0( )-10(pr)7(o)10(pag)10(ati)6(o)10(n)]TJ T* 0.003 Tc 0.219 Tw [(mech)9(ani)5(s)13(m)-4(. I)11(f)1( i)5(m)-4(i)5(t)11(ati)5(on i)5(s)13( m)6(u)-1(ch )10(mor)6(e)9( l)5(i)5(k)3(el)5(y)13( than i)5(n)9(nov)13(ati)5(on,)11( i)5(t)1( i)5(s)3( )-10(si)5(g)9(n)-1(i)5(f)-9(i)5(c)3(a)9(n)-1(tl)5(y)]TJ T* -0.002 Tc 0.234 Tw [(e)-6(a)-6(s)-2(ie)-6(r to com)-9(p)-6(ute)-6( lon)-6(g)4(-ru)-6(n)-6( e)-6(q)4(u)-6(ilib)-6(riu)-6(m)-9(. )10(Th)-6(e)-6( lo)-6(n)-6(g)4(-ru)-6(n lim)-9(it con)-6(t)-4(a)-6(i)10(n)-6(s)-2( on)-6(ly)8( )-10(p)-6(u)-6(r)1(e)]TJ T* 0.004 Tc 0.158 Tw [(str)7(a)0(teg)10(i)6(es. )10(C)6(a)0(l)6(c)4(ul)6(a)10(t)2(i)6(ons c)14(an )10(be )10(ma)10(de )10(by)14( compar)7(i)16(n)0(g)10( pai)6(r)7(s)4( o)10(f)-8( )10(pur)7(e s)14(t)2(r)7(a)0(teg)10(i)6(es t)12(o)]TJ T* 0.003 Tc -0.001 Tw [(see h)9(o)-1(w)15( w)15(e)-1(ll)5( they)13( do ag)9(ai)5(nst)11( on)9(e a)9(not)11(her)6(. )-10(A)10( )-10(su)9(ff)-9(i)5(c)3(i)5(e)9(nt )-10(c)13(ondi)5(ti)15(on for)6( )-10(a )-10(pr)16(o)9(f)-9(i)5(l)5(e)-1( )-10(t)11(o)-1( )-10(b)9(e)]TJ T* -0.002 Tc 0.134 Tw [(th)-6(e)-6( )10(u)-6(n)-6(i)0(qu)-6(e)-6( lon)-6(g)4(-ru)-6(n)-6( e)-6(q)4(u)-6(ilib)-6(riu)-6(m)-9( is t)6(h)-6(a)-6(t)-4( it)6( b)-6(e)4(a)-6(t)-4( )-10(a)-6(ll o)-6(t)-4(he)-6(rs )-10(in)-6( )-10(pa)-6(irw)10(i)0(se)-6( )-10(co)-6(n)-6(t)-4(e)-6(s)-2(ts. A)]TJ T* 0.003 Tc -0.011 Tw [(num)6(ber)6( o)9(f)-9( )-10(ex)13(am)6(pl)5(es ar)6(e )-10(co)9(nsi)5(der)6(e)9(d)-1(.)]TJ 0 -4.47 TD -0.001 Tw [(N)5(o)-1(te: t)11(h)-1(i)5(s)3( v)13(e)-1(r)6(s)3(i)5(on i)5(s)3( pr)6(el)5(i)5(m)-4(i)5(n)9(ar)6(y)13( and i)5(n)-1(c)13(o)-1(m)6(p)-1(l)5(e)-1(te)9(.)]TJ /F3 1 Tf 0 -3.16 TD 0 Tc 0 Tw ( )Tj ET 1 i 90.09 102.09 143.88 -0.48 re f BT 6.48 0 0 6.48 90.09 90.57 Tm (1)Tj 9.96 0 0 9.96 93.33 86.01 Tm 0.004 Tc -0.001 Tw [( We are g)10(r)0(at)5(ef)12(u)10(l)5( t)5(o)-2( su)10(pport)5( f)12(r)0(om)23( Na)-10(t)5(i)5(o)-2(n)10(a)2(l)5( S)6(c)-10(i)5(e)2(n)10(ce F)6(o)-14(u)10(n)10(d)-2(at)5(i)5(o)-2(n)10( )-12(Gran)10(ts)7(.)]TJ 6.48 0 0 6.48 90.09 79.05 Tm 0 Tc 0 Tw (2)Tj 9.96 0 0 9.96 93.33 74.49 Tm 0.004 Tc -0.001 Tw [( Depart)5(m)23(e)-10(n)10(t)-7(s)7( of)12( Econ)10(o)-14(m)11(i)5(c)2(s)7( UCLA an)10(d Pri)5(n)10(cet)5(on)10(.)]TJ ET endstream endobj 35 0 obj << /ProcSet [/PDF /Text ] /Font << /F1 36 0 R /F2 37 0 R /F3 38 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 41 0 obj << /Length 5816 >> stream BT /F3 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc 0 Tw (1)Tj /F1 1 Tf 14.04 0 0 14.04 90.09 692.01 Tm -0.001 Tc -0.003 Tw (1. Introduction)Tj /F3 1 Tf 12 0 0 12 126.09 669.09 Tm 0 Tc 0.18 Tw [(I)13(n)0( )10(two )10(influ)-10(e)4(ntial )10(papers )10(K)-8(a)4(ndori, Mailath )-10(and Rob [)-7(1993])-7( and Young)10( [)-7(1993])]TJ -3 -1.67 TD 0.14 Tw [(showed how introducin)-10(g)10( r)-7(a)4(ndom innovations \(mutations\) into a model of evolutionar)-17(y)]TJ T* 0.001 Tc 0.029 Tw [(a)5(d)1(justme)5(nt e)5(n)1(a)5(b)1(le)5(s pre)5(d)1(ic)5(tions a)5(b)-9(out whic)5(h of se)5(vera)5(l stric)5(t)-1( N)-7(a)5(sh )-10(e)5(quilibria)5( )-10(will )-10(oc)5(c)5(u)-9(r )-10(in)]TJ 0 -1.66 TD 0 Tc 0.07 Tw [(the ver)-17(y)20( lon)-10(g)10( run. K)-8(e)-16(y)20( to this result is )-10(the )-10(possibilit)-12(y)30( )-10(that )-10(strateg)10(i)-2(es )-10(th)-10(at )-10(perfo)-10(rm )-10(poorl)-22(y)]TJ 0 -1.67 TD 0.03 Tw [(ma)-6(y)20( b)-10(e)4( introduced into the population in sufficient numbe)-6(rs )-10(throu)-10(g)10(h )-10(innovation )-10(that )-10(the)-16(y)]TJ T* 0.001 Tc 0.379 Tw [(be)5(g)11(i)-1(n to perform w)-7(e)5(ll. He)5(re)5( we)5( )-10(e)5(x)-9(a)5(mine)5( imita)5(tion a)5(s)0( a)5(n)1( a)5(lte)5(rna)5(tive)5( propaga)5(tion)]TJ 0 -1.66 TD 0 Tc 0.07 Tw [(mechanism. A striking)10( )-10(fact is that if imitation is much more likel)-12(y)20( than )-10(innov)-10(ation, )-10(it )-10(is)]TJ 0 -1.67 TD 0.001 Tc 0.179 Tw [(sig)11(n)1(ific)5(a)5(n)1(tl)-21(y)21( ea)5(sie)5(r)4( to find the)5( lon)-9(g)11(-run e)5(quilibrium. F)7(i)-1(rst, the)5( lon)-9(g)11(-run limit c)5(onta)5(i)-1(ns)]TJ T* -0.001 Tc 0.261 Tw [(onl)-13(y)19( pure)-7( strate)-7(g)9(i)-3(es. Se)-7(cond, cal)-13(culations can be ma)-7(de b)-21(y)19( comp)-11(arin)-11(g)9( pairs of )-10(pu)-11(re)]TJ 0 -1.66 TD 0.001 Tc 0.169 Tw [(stra)5(teg)11(i)-1(e)5(s)0( to se)5(e)5( how )-10(we)5(ll the)5(y)11( )-10(do aga)5(i)-1(nst one)5( a)5(nothe)5(r. )-10(One)5( useful re)5(sult is )-10(tha)5(t)-1( )-10(it )-10(is)]TJ 0 -1.67 TD 0.209 Tw [(suffic)5(i)-1(e)5(n)1(t )10(tha)5(t)-1( )10(a)5( )10(stra)5(t)-11(e)-5(g)-9(y)21( )10(profile)5( )10(b)-9(e)5(a)5(t)-1( a)5(ll othe)5(rs in pa)5(irwise)5( c)5(onte)5(s)0(ts. As w)-7(e)5( illustra)5(te)]TJ T* 0.039 Tw [(throug)11(h e)5(x)-9(a)5(m)-1(ple)5(s)0(, this is implie)5(d b)-9(y)21(, but more)5( like)5(l)-21(y)21( to be)5( sa)5(tisfie)5(d)1( tha)5(n, )-10(the)5( )-20(c)5(r)4(ite)5(rion )-10(of)]TJ /F4 1 Tf 0 -1.66 TD 0 Tc 0 Tw [(\275-dominance propos)-11(ed by)10( )-10(Morris, Rob and Shin [)-7(1993])-7(.)]TJ 3 -1.67 TD 0.001 Tc 0.019 Tw [(This work ste)5(m)-1(s from our a)5(d)1(mira)5(tion of the)5( e)5(x)-9(isting)11( the)5(o)1(r)-16(y)21(, a)5( d)-9(e)5(sire)5( )-10(to )-10(a)5(pply)11( )-20(it )-10(to)]TJ -3 -1.67 TD 0 Tc 0.11 Tw [(interesting)10( games, )10(and )10(our dissatisf)-7(action with innovation as a propa)-6(gation mechanism.)]TJ 0 -1.66 TD 0.07 Tw [(To us, the theor)-17(y)20( of evolution with persistent r)-7(a)4(ndomness is a theor)-17(y)20( of th)-10(e propa)-6(gation)]TJ 0 -1.67 TD 0.05 Tw [(of )10(ideas )10(throu)-10(g)10(h )10(a population. K)-8(e)-16(y)20( to anal)-22(y)30(z)-6(in)-10(g)10( lon)-10(g)10(-ru)-10(n d)-20(y)20(namics is the possibilit)-12(y)20( that)]TJ T* -0.001 Tc 0.021 Tw [(bad )10(ideas )10(ma)-17(y)19( )10(spr)-8(ead, cha)-7(n)-11(g)9(i)-3(n)-11(g)9( which ide)-7(a)3(s ar)-8(e )-10(g)9(ood and which )-10(ar)-8(e bad. To think of this)]TJ 0 -1.66 TD 0 Tc 0.11 Tw [(propa)-6(g)10(a)4(tion takin)-10(g)10( plac)-6(e throu)-10(g)10(h random innovations )-10(se)-6(ems )-10(hig)10(h)0(l)-22(y)20( )-10(unsatisfa)-6(ctor)-17(y)20(.)0( )-20(I)13(t)-2( )-10(is)]TJ 0 -1.67 TD 0.001 Tc 0.219 Tw [(ha)5(rd )10(to )10(think )10(of )10(a)5(n)-19(y)21( sig)11(n)1(ifi)-11(c)5(a)5(n)1(t c)5(h)-9(a)5(n)-9(g)11(e)5(s in institutions tha)5(t)-1( ha)5(ve)5( oc)5(c)5(u)1(rre)5(d)1( in huma)5(n)]TJ T* -0.001 Tc 0.101 Tw [(histor)-8(y)19( be)-7(cause la)-7(r)-8(g)9(e numbe)-7(rs of people simpl)-23(y)19( happ)-11(en to )-10(have )-10(tried )-10(th)-11(e )-10(same )-10(thin)-11(g)9( )-10(at)]TJ 0 -1.66 TD 0.001 Tc 0.109 Tw [(more)5( )10(or )10(le)5(ss )10(the)5( )10(sa)5(me)5( )10(time)5(. )10(Ra)5(ther, we)5( b)-9(e)5(lie)5(ve)5( tha)5(t)-1( idea)5(s a)5(r)-6(e)5( sprea)5(d)1( throu)-9(g)11(h imita)5(tion.)]TJ 0 -1.67 TD 0 Tc 0.15 Tw [(One)4( e)4(x)-10(a)4(m)-2(ple)4( is the)4( c)4(h)0(a)4(nge)4( o)-10(f)3( institutions throug)10(h )-10(c)4(i)-2(vil )-10(disobe)4(die)4(n)0(c)4(e)4(,)0( )-20(a)4(s)-1( )-10(oc)4(c)4(u)-10(rre)4(d, )-20(for)]TJ T* 0.001 Tc 0.209 Tw [(e)5(x)-9(a)5(m)-1(ple)5(,)1( )10(in Ea)5(st Ge)5(rma)5(n)1(y)11(.)-9( )-10(I)14(n)1(itia)5(ll)-11(y)21( )-10(a)5( sma)5(ll numbe)5(r of p)-9(e)5(ople)5( prote)5(s)0(te)5(d the e)5(x)-9(isting)]TJ 0 -1.66 TD 0 Tc 0.04 Tw [(g)10(ove)-6(rnment. I)13(t)-2( )10(seems likel)-22(y)20( that r)-7(a)4(tional calculation would show that this was )-10(a bad ide)-6(a)]TJ 0 -1.67 TD 0.02 Tw [(\226 )10(that )10(the )10(probabilit)-12(y)20( )10(of )10(bein)-10(g punished severel)-22(y)20( was substantial. )-10(B)7(u)0(t others imitated, and)]TJ T* [(once )10(the idea spread sufficientl)-22(y)20( widel)-22(y)20(, the p)-10(r)3(obabilit)-12(y)20( o)-10(f)3( punishment dropped, and )-10(civil)]TJ 0 -1.66 TD -0.001 Tc 0.001 Tw [(disobedience be)-7(came )-10(a best r)-8(e)3(sponse.)]TJ 3 -1.67 TD 0.051 Tw [(I)12(n)-1( addition )10(to the work mentioned abov)-11(e, there )-10(are s)-12(e)3(ver)-8(a)3(l other p)-11(a)3(pers that h)-11(a)3(ve)]TJ -3 -1.67 TD 0 Tc 0.01 Tw [(a connection to our results. B)7(e)-6(r)-7(g)10(in and )-10(L)11(i)-2(pman [)-7(1994])-7( )-10(show )-10(that )-10(the )-10(relative )-10(probabilities)]TJ ET endstream endobj 42 0 obj << /ProcSet [/PDF /Text ] /Font << /F1 36 0 R /F3 38 0 R /F4 43 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 44 0 obj << /Length 9800 >> stream BT /F3 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc 0 Tw (2)Tj -17.75 -3 TD 0.001 Tc -0.001 Tw [(of diffe)5(re)5(nt t)-11(y)21(p)-9(e)5(s of noise)5( ca)5(n ma)5(ke)5( )-10(a)5(n)1( e)5(n)1(o)-9(r)4(mous )-10(diffe)5(re)5(nce)5( )-10(in )-10(long)11(-ru)-9(n )-10(e)5(quilibrium; )-10(he)5(re)]TJ 0 -1.66 TD 0 Tc 0.1 Tw [(we)4( )10(e)4(x)-10(plore)4( )10(on )10(pa)4(rtic)4(ular )10(the)4(o)0(r)-17(y)20( of ho)-10(w those)4( re)4(l)-12(a)4(tive)4( proba)4(bilitie)4(s a)4(r)-7(e)4( de)4(te)4(rmine)4(d. Va)4(n)]TJ 0 -1.67 TD 0.16 Tw [(Damme )10(and )10(W)-6(e)4(ibull )10([)-7(1998])-7( )10(s)9(t)-2(ud)-10(y)30( a model in which it is costl)-12(y)20( to r)-7(e)4(duce )-10(erro)-10(rs, and)]TJ T* -0.001 Tc 0.111 Tw [(show )10(that )10(the )10(basic )10(2x)-11(2 )10(results on risk dominance go throu)-11(g)9(h. )-10(B)-14(y)19( wa)-17(y)19( of )-10(contrast, our)]TJ 0 -1.66 TD 0.131 Tw [(focus is on lar)-8(g)9(e)-7(r)2( more complex)-11( games. Our )-10(result about )-10(winnin)-11(g)9( )-10(pairwise )-10(co)-11(ntests )-10(is)]TJ 0 -1.67 TD 0 Tc 0.32 Tw [(connected to )-10(a result of K)-8(a)4(ndori and Rob [)-7(1993])-7(. W)-6(e)4( ex)-10(p)10(l)-2(ain this connection )-10(in)]TJ T* 0 Tw [(conjunction with introducing)10( our o)-10(w)2(n result about winnin)-10(g)10( pairwis)-11(e)4( contests.)]TJ /F1 1 Tf 14.04 0 0 14.04 90.09 552.09 Tm -0.002 Tc -0.002 Tw [(2.)-6( )-8(The M)-7(odel)]TJ /F3 1 Tf 12 0 0 12 126.09 529.05 Tm 0 Tc 0.16 Tw [(W)-6(e)4( stud)-10(y)20( a s)-21(y)20(mmetric norm)-12(a)4(l form )-20(g)10(a)4(me )-20(with )-10(a )-10(sing)10(le )-10(popul)-12(ation )-10(of )-10(pla)-16(y)20(ers.)]TJ -3 -1.67 TD -0.002 Tc 0.132 Tw [(There )10(i)-4(s)-3( a )-10(fi)-4(ni)-4(t)-4(e)2( num)-4(ber )]TJ /F5 1 Tf 10.67 0 TD 0 Tc 0 Tw (3)Tj /F3 1 Tf 0.91 0 TD -0.001 Tc 0.131 Tw [( of pure strate)-7(g)9(i)-13(es, and w)-9(e)3( write )]TJ /F5 1 Tf 11.97 0 0 11.97 398.49 509.01 Tm 1.323 Tc (S3)Tj /F6 1 Tf 0.792 0 TD 0 Tc 0 Tw (\211)Tj /F3 1 Tf 12 0 0 12 430.53 509.01 Tm -0.002 Tc 0.132 Tw [( fo)-12(r a t)-24(y)18(pical pur)-9(e)]TJ -28.37 -1.66 TD -0.001 Tc 0.001 Tw [(strate)-7(g)-11(y)19(. Notice that w)-9(e)3( use the s)-12(a)3(me )-10(s)-22(y)29(mbol )-20(for )-10(the )-10(numbe)-7(r )-10(of )-10(pur)-8(e )-10(strate)-7(g)9(i)-3(es )-20(and )-10(the )-10(set)]TJ 0 -1.67 TD 0 Tc 0.15 Tw [(of pure)4( stra)4(t)-12(e)-6(g)10(i)-2(e)4(s)-1(. Mix)-10(e)4(d stra)4(te)4(g)10(i)-12(e)4(s)-1( a)4(r)-7(e)4( ve)4(c)4(t)-2(ors o)-10(f)3( proba)4(bilitie)4(s de)4(note)4(d)0( b)-20(y)20( )]TJ /F7 1 Tf 11.97 0 0 11.97 470.97 469.05 Tm 0 Tw (T)Tj /F6 1 Tf 0.9424 0 TD 0.28 Tc (\2114)Tj /F3 1 Tf 12 0 0 12 505.53 469.05 Tm 0 Tc 0.16 Tw (. A)Tj -34.62 -1.67 TD 0.001 Tc 0.089 Tw [(mix)-9(e)5(d)1( stra)5(te)5(g)-9(y)21( is c)5(a)5(lle)5(d )]TJ /F8 1 Tf 10.07 0 TD 0 Tc (pure)Tj /F3 1 Tf 1.83 0 TD 0.09 Tw [( if it puts unit wei)-12(g)10(ht on a sin)-10(g)10(le pure str)-7(a)4(te)-6(g)-10(y)20(; )-10(we )-10(d)-10(e)4(note)]TJ -11.9 -1.66 TD -0.001 Tc 0.001 Tw [(the mix)-11(ed strateg)-11(y)19( cor)-8(r)2(espondin)-11(g)9( to the pur)-8(e strateg)-11(y)19( )]TJ /F5 1 Tf 21.71 0 TD 0 Tc 0 Tw (S)Tj /F3 1 Tf 0.76 0 TD [( also b)-10(y)20( )]TJ /F5 1 Tf 3.52 0 TD (S)Tj /F3 1 Tf 0.76 0 TD 0.01 Tw [(. The)4( utilit)-12(y)30( of a)4( pl)-12(a)-16(y)20(e)4(r)]TJ -26.75 -1.67 TD 0.07 Tw [(depends on his own pure str)-7(a)4(te)-6(g)-10(y)20( and th)-10(e mix)-10(ed )-10(strateg)-10(y)20( )-10(pla)-16(y)20(e)-6(d)0( )-10(b)-20(y)20( )-10(the )-10(population. )-20(I)13(t)-2( )-10(is)]TJ T* [(writte)4(n )]TJ /F9 1 Tf 3.94 0 TD 0.33 Tc [(\010\014)-370(\011)]TJ /F5 1 Tf -0.55 0 TD 0.32 Tc (US)Tj /F7 1 Tf 1.66 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 1.17 0 TD 0.002 Tc 0.138 Tw [(. We)6( a)6(ssume)6( tha)6(t)0( )]TJ /F5 1 Tf 8.2 0 TD 0 Tc 0 Tw (U)Tj /F3 1 Tf 0.83 0 TD 0.14 Tw [( is continuous in )]TJ /F7 1 Tf 7.6 0 TD 0 Tw (T)Tj /F3 1 Tf 0.88 0 TD -0.001 Tc 0.141 Tw [(. A protot)-13(y)19(p)-1(ic)-7(al ex)-11(ample )-10(is )-10(a)]TJ -23.73 -1.66 TD 0 Tc 0.36 Tw [(g)10(a)4(m)-12(e)4( in which pla)-16(y)20(e)-6(r)3(s from diff)-7(erent populations a)-6(r)3(e r)-7(a)4(ndoml)-12(y)20( )-10(mat)-12(c)4(hed )-10(to )-10(pla)-16(y)]TJ 0 -1.67 TD -0.001 Tc 0.001 Tw [(particular pla)-17(y)19(e)-7(r)2( roles; we)-7( discuss this along)9( )-10(with other ex)-11(amples below.)]TJ 3 -1.67 TD -0.003 Tc 0.103 Tw (There are )Tj /F5 1 Tf 4.4 0 TD 0 Tc 0 Tw (M)Tj /F3 1 Tf 1.16 0 TD 0.09 Tw [( pla)-6(y)20(e)-6(r)3(s in the population, e)-6(ach of w)-8(hom pla)-6(y)20(s )-20(a )-10(pure )-10(str)-7(a)4(te)-6(g)-10(y)20(. )-10(At)]TJ -8.56 -1.66 TD 0.002 Tc [(time)6( )]TJ /F5 1 Tf 11.931 0 0 11.931 117.09 309.09 Tm 0 Tc 0 Tw (T)Tj /F3 1 Tf 12 0 0 12 125.13 309.09 Tm 0.06 Tw [( we denote the distribution of strate)-6(g)10(i)-2(es in the population b)-20(y)20( )]TJ /T1 1 Tf 8.355 0 0 8.355 433.65 305.49 Tm 0 Tw (T)Tj /F7 1 Tf 11.975 0 0 11.975 427.17 309.09 Tm (T)Tj /F6 1 Tf 1.2426 0 TD 0.28 Tc (\2114)Tj /F3 1 Tf 12 0 0 12 464.73 309.09 Tm 0.002 Tc 0.078 Tw [(. I)15(n)2(itia)6(ll)-20(y)22( )10(a)6(t)]TJ -31.22 -1.67 TD [(time)6( )]TJ /F9 1 Tf 11.931 0 0 11.931 138.93 289.05 Tm 0 Tc 0 Tw (\020)Tj /F5 1 Tf -1.8808 0 TD (T)Tj /F6 1 Tf 0.7543 0 TD (\036)Tj /F3 1 Tf 12 0 0 12 147.57 289.05 Tm 0.01 Tw [( there is a )-10(g)10(i)-2(ven )-10(initial )-10(condition )]TJ /T2 1 Tf 8.355 0 0 8.355 316.53 285.21 Tm 0 Tw (\020)Tj ET q 1 i 309.45 298.05 14.64 -15.36 re W* n BT /F7 1 Tf 11.97 0 0 11.97 309.45 289.05 Tm (T)Tj ET Q BT /F3 1 Tf 12 0 0 12 324.09 289.05 Tm 0.02 Tw [(. )-10(I)23(n)0( subs)-11(equent periods )]TJ /T3 1 Tf 8.355 0 0 8.355 447.57 285.45 Tm 0 Tw (T)Tj /F7 1 Tf 11.97 0 0 11.97 441.09 289.05 Tm (T)Tj /F3 1 Tf 12 0 0 12 453.69 289.05 Tm 0.001 Tc 0.019 Tw [( is de)5(te)5(rmine)5(d)]TJ -30.3 -1.67 TD 0 Tc (from )Tj /T4 1 Tf 8.355 0 0 8.355 134.97 265.05 Tm 0 Tw (\021)Tj /T5 1 Tf -1.1633 0 TD (T)Tj /F7 1 Tf 11.97 0 0 11.97 118.77 269.01 Tm (T)Tj /T6 1 Tf 8.355 0 0 8.355 128.85 265.05 Tm (\016)Tj /F4 1 Tf 12 0 0 12 141.33 269.01 Tm 0.001 Tc -0.001 Tw [( a)5(c)-5(c)5(o)1(rdin)-9(g)11( to the)5( followin)-9(g)11( \223)5(imita)5(tive)5(\224)5( pro)-9(c)5(e)5(ss.)]TJ -4.27 -1.66 TD 0 Tc (1\))Tj /F2 1 Tf 0.83 0 TD 0 Tw ( )Tj /F4 1 Tf 0.67 0 TD -0.002 Tc 0.002 Tw [(One pl)-4(a)-18(y)18(er )]TJ /F5 1 Tf 11.931 0 0 11.931 166.05 249.09 Tm 0 Tc 0 Tw (I)Tj /F4 1 Tf 12 0 0 12 173.01 249.09 Tm [( is chosen at ra)-6(ndom. Onl)-22(y)20( this pla)-6(y)20(e)-6(r)3( ch)-10(an)-10(g)10(e)4(s his strate)-6(g)-10(y)20(.)]TJ -6.91 -1.67 TD (2\))Tj /F2 1 Tf 0.83 0 TD ( )Tj /F4 1 Tf 0.67 0 TD 0.001 Tc 0.179 Tw [(With proba)5(bilit)-11(y)31( )]TJ /F5 1 Tf 7.34 0 TD 0 Tc 0 Tw (#)Tj /F7 1 Tf 0.86 0 TD (F)Tj /F4 1 Tf 0.72 0 TD 0.006 Tc 0.174 Tw [( p)6(l)4(ay)26(er)9( )]TJ /F5 1 Tf 11.931 0 0 11.931 257.49 229.05 Tm 0 Tc 0 Tw (I)Tj /F4 1 Tf 12 0 0 12 264.45 229.05 Tm -0.001 Tc 0.181 Tw [( chooses from )]TJ /F5 1 Tf 6.58 0 TD 0 Tc 0 Tw (3)Tj /F4 1 Tf 0.91 0 TD 0.19 Tw [( randoml)-12(y)20( usin)-10(g)10( the prob)-10(abilities)]TJ /T4 1 Tf 8.355 0 0 8.355 126.69 205.05 Tm 0 Tw (\021)Tj /T5 1 Tf -1.1633 0 TD (T)Tj /F7 1 Tf 11.97 0 0 11.97 110.49 209.01 Tm (T)Tj /T6 1 Tf 8.355 0 0 8.355 120.57 205.05 Tm (\016)Tj /F4 1 Tf 12 0 0 12 133.05 209.01 Tm 0.001 Tc 0.089 Tw [(. )10(This is c)5(a)5(lle)5(d )]TJ /F8 1 Tf 6.43 0 TD (imitation)Tj /F4 1 Tf 3.62 0 TD -0.001 Tc 0.091 Tw [(: strateg)9(i)-3(es a)-7(r)2(e chos)-12(en in proportion to how fr)-8(equentl)-23(y)]TJ -12.13 -1.66 TD 0 Tc 0 Tw [(the)-6(y)20( w)-8(e)4(re pl)-12(a)-16(y)20(ed in the population in the previous p)-10(e)4(riod.)]TJ -1.5 -1.67 TD (3\))Tj /F2 1 Tf 0.83 0 TD ( )Tj /F4 1 Tf 0.67 0 TD 0.001 Tc 0.049 Tw [(With proba)5(bilit)-11(y)31( )]TJ /T7 1 Tf 8.379 0 0 8.379 200.13 173.85 Tm 0 Tc 0 Tw (N)Tj /F7 1 Tf 12 0 0 12 194.61 169.05 Tm (F)Tj /F4 1 Tf 1.2 0 TD 0.006 Tc 0.044 Tw [( p)6(l)4(ay)26(er)9( )]TJ /F5 1 Tf 11.931 0 0 11.931 248.25 169.05 Tm 0 Tc 0 Tw (I)Tj /F4 1 Tf 12 0 0 12 255.21 169.05 Tm -0.001 Tc 0.051 Tw [( chooses from )]TJ /F5 1 Tf 6.18 0 TD 0 Tc 0 Tw (3)Tj /F4 1 Tf 0.91 0 TD 0.06 Tw [( randoml)-12(y)20( with equ)-10(a)4(l probabilities of)]TJ /F9 1 Tf -19.19 -1.67 TD 0.06 Tc (\021\017)Tj /F5 1 Tf 1.15 0 TD 0 Tc 0 Tw (3)Tj /F4 1 Tf 0.94 0 TD -0.001 Tc 0.251 Tw [( of choosing)9( )-10(ea)-7(ch strate)-7(g)9(y)9(.)-11( This is called )]TJ /F8 1 Tf 18.51 0 TD 0.001 Tc [(inno)-9(v)5(a)1(tion)]TJ /F4 1 Tf 4.29 0 TD -0.002 Tc 0.262 Tw [(:)-4( )10(st)-4(rat)-4(e)-8(g)8(i)-4(es ar)-9(e pi)-4(cked)]TJ -25.05 -1.66 TD -0.001 Tc 0.001 Tw [(re)-7(g)9(a)3(rdl)-13(e)3(ss of how widel)-23(y)19( used th)-11(e)-17(y)19( ar)-8(e, or how suc)-7(cessful the)-17(y)19( )-10(ar)-8(e.)]TJ -1.5 -1.67 TD 0 Tc (4\))Tj /F2 1 Tf 0.83 0 TD 0 Tw ( )Tj /F4 1 Tf 0.67 0 TD 0.001 Tc 0.179 Tw [(With proba)5(bilit)-11(y)31( )]TJ /F9 1 Tf 7.41 0 TD 0 Tc 0 Tw (\021)Tj /T8 1 Tf 8.379 0 0 8.379 251.73 113.85 Tm (N)Tj /F5 1 Tf 12 0 0 12 215.49 109.05 Tm (#)Tj /F7 1 Tf 0.86 0 TD 1.23 Tc (FF)Tj /F6 1 Tf -1.73 0 TD 1.65 Tc (\016\016)Tj /F4 1 Tf 4.59 0 TD 0.006 Tc [(p)6(l)4(ay)26(er)9( )]TJ /F5 1 Tf 11.931 0 0 11.931 297.45 109.05 Tm 0 Tc (I)Tj /F4 1 Tf 12 0 0 12 304.41 109.05 Tm 0.19 Tw [( chooses randoml)-22(y)20( with equal prob)-10(abilities)]TJ -16.36 -1.67 TD 0 Tw [(among)10( the s)-11(e)4(t of strate)-6(g)10(i)-2(es th)-10(at solve the problem used b)-20(y)20( the most pla)-16(y)20(e)-6(r)3(s)]TJ ET endstream endobj 45 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F1 36 0 R /F2 37 0 R /F3 38 0 R /F4 43 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /T1 51 0 R /T2 52 0 R /T3 53 0 R /T4 54 0 R /T5 55 0 R /T6 56 0 R /T7 57 0 R /T8 58 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 59 0 obj << /Length 7945 >> stream BT /F3 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc 0 Tw (3)Tj /T9 1 Tf 6.008 0 0 6.008 288.21 700.65 Tm (\021)Tj /T10 1 Tf 8.391 0 0 8.391 351.57 704.13 Tm (\021)Tj -9.1388 -0.0858 TD 1.698 Tc [(\\\010)1203(\011)945(\020)]TJ /F9 1 Tf 12.021 0 0 12.021 248.25 708.09 Tm 0 Tc [(MAX)-4233(\010)-379(\014)-1836(\011)]TJ /T11 1 Tf 6.008 0 0 6.008 281.37 700.65 Tm (T)Tj /T12 1 Tf 8.391 0 0 8.391 341.85 704.13 Tm (T)Tj -8.4952 -0.0858 TD 2.411 Tc (SS)Tj /F5 1 Tf 12.021 0 0 12.021 314.85 708.09 Tm 0.319 Tc (US)Tj /T13 1 Tf 8.391 0 0 8.391 276.93 703.41 Tm 0 Tc (T)Tj ET q 1 i 335.37 720.09 24 -18.36 re W* n BT /F7 1 Tf 12.021 0 0 12.021 335.37 708.09 Tm (T)Tj ET Q BT /T14 1 Tf 6.008 0 0 6.008 283.89 700.65 Tm (\016)Tj /T15 1 Tf 8.391 0 0 8.391 345.45 704.13 Tm (\016)Tj -5.2058 -0.0858 TD (\037)Tj /T16 1 Tf -3.6612 0.0286 TD 2.339 Tc (%%)Tj ET q 1 i 326.01 720.09 24 -17.88 re W* n BT /F10 1 Tf 12.021 0 0 12.021 326.01 708.45 Tm 0 Tc (%)Tj ET Q BT /F3 1 Tf 12 0 0 12 363.57 708.09 Tm 0 Tc (.)Tj -22.79 -2.75 TD 0.001 Tc 0.049 Tw [(This is c)5(a)5(lle)5(d a)5( )]TJ /F8 1 Tf 6.47 0 TD -0.001 Tc 0.051 Tw [(relative best respons)-12(e)]TJ /F3 1 Tf 8.82 0 TD 0.061 Tw [(: )10(it )10(is the best response amon)-11(g)9( those strat)-13(e)-7(g)9(i)-3(es that)]TJ -15.29 -1.67 TD 0.001 Tw [(are a)-7(c)3(tuall)-23(y)19( used b)-21(y)19( the pa)-7(rticular population.)]TJ 1.5 -1.67 TD 0.211 Tw [(Observe that this proc)-7(ess )-10(g)9(i)-3(ves rise to )-10(a )-10(M)-12(a)3(rkov )-10(pro)-11(cess )]TJ /F5 1 Tf 25.05 0 TD 0 Tc 0 Tw (-)Tj /F3 1 Tf 1.31 0 TD -0.002 Tc 0.222 Tw [( on t)-4(h)-2(e st)-4(at)-4(e space)]TJ /T17 1 Tf 8.355 0 0 8.355 100.77 619.89 Tm 0 Tc 0 Tw (M)Tj /F6 1 Tf 11.97 0 0 11.97 92.37 615.09 Tm 1.002 Tc [(4\207)711(4)]TJ /F3 1 Tf 12 0 0 12 137.13 615.09 Tm -0.002 Tc 0.192 Tw [( consi)-4(s)-3(t)-4(i)-4(n)-2(g)8( of al)-4(l)-4( m)-4(i)-4(x)-12(ed st)-4(rat)-4(e)2(g)8(i)-14(es consi)-4(s)-3(t)-4(e)2(nt)-4( wi)-4(t)-4(h)-2( t)-4(h)-2(e )-10(gri)-4(d)-2( )-10(i)-4(nduced )-10(b)-22(y)18( )-20(each)]TJ -3.92 -1.67 TD 0.002 Tw [(pl)-4(a)-8(y)18(e)-8(r)1( pl)-4(a)-18(y)18(i)-4(n)-12(g)8( a )-10(pu)-12(re )-10(st)-4(rat)-14(e)-8(g)-12(y)18(. )-10(Not)-4(e)2( )-10(t)-4(h)-2(at)-4( )-10(al)-4(l)-4( )-10(pur)-9(e )-10(st)-4(rat)-4(e)-8(g)8(i)-4(es )-20(are )-10(i)-4(n)-2( )]TJ /T18 1 Tf 8.379 0 0 8.379 415.53 599.85 Tm 0 Tc 0 Tw (M)Tj /F6 1 Tf 12 0 0 12 407.13 595.05 Tm (4)Tj /F3 1 Tf 1.56 0 TD -0.001 Tc 0.011 Tw [(. The proc)-7(ess )]TJ /F5 1 Tf 5.78 0 TD 0 Tc 0 Tw (-)Tj /F3 1 Tf 1.31 0 TD 0.002 Tc 0.008 Tw [( is)]TJ -35.07 -1.67 TD 0.001 Tc 0.269 Tw [(positive)5(l)-11(y)31( )-10(rec)5(u)1(rre)5(n)1(t, a)5(nd so ha)5(s a)5( uniqu)-9(e)5( inva)5(ria)5(n)1(t distribution )]TJ /T19 1 Tf 8.379 0 0 8.379 430.29 579.81 Tm 0 Tc 0 Tw (F)Tj /F7 1 Tf 12 0 0 12 422.61 575.01 Tm (N)Tj /F3 1 Tf 1.2 0 TD 0.28 Tw [(. Our )-10(g)10(o)0(a)4(l)-2( is to)]TJ -28.91 -1.66 TD -0.003 Tc [(chara)-9(c)1(t)-5(e)1(ri)-5(z)-9(e)1( )]TJ /T20 1 Tf 8.355 0 0 8.355 209.01 551.25 Tm 0 Tc 0 Tw (\020)Tj /F9 1 Tf 11.975 0 0 11.975 178.65 555.09 Tm (LIM)Tj /T21 1 Tf 8.355 0 0 8.355 223.53 559.89 Tm (F)Tj -3.3176 -1.034 TD (F)Tj /F7 1 Tf 11.975 0 0 11.975 153.69 555.09 Tm 4.601 Tc (NN)Tj /T22 1 Tf 8.355 0 0 8.355 200.13 551.25 Tm 0 Tc (l)Tj /F6 1 Tf 11.975 0 0 11.975 165.09 555.09 Tm (w)Tj /F3 1 Tf 12 0 0 12 231.09 555.09 Tm (.)Tj -10.25 -1.67 TD 0.4 Tw [(Our main assumption is that imitation is )10(much more likel)-12(y)20( than innovation.)]TJ -1.5 -1.67 TD -0.004 Tc [(S)-8(p)-4(eci)-6(fi)-6(cal)-6(l)-26(y)]TJ /F11 1 Tf 0 -2.16 TD 0.001 Tc -0.001 Tw [(Unlikely In)7(novation:)]TJ /F8 1 Tf 8.87 0 TD 0 Tc 0 Tw ( )Tj /F5 1 Tf 11.931 0 0 11.931 201.45 489.09 Tm 1.449 Tc (NM)Tj /F6 1 Tf 0.9454 0 TD 0 Tc (\037)Tj /F8 1 Tf 12 0 0 12 239.37 489.09 Tm (.)Tj /F3 1 Tf -12.44 -2.17 TD 0.001 Tc 0.179 Tw [(I)14(n)1( p)-9(a)5(rtic)5(ula)5(r)4( this mea)5(n)1(s tha)5(t)-1( a)5(s)0( )]TJ /F9 1 Tf 11.931 0 0 11.931 281.73 463.05 Tm 0 Tc 0 Tw (\020)Tj /F7 1 Tf -2.1825 0 TD (F)Tj /F6 1 Tf 0.8147 0 TD (l)Tj /F3 1 Tf 12 0 0 12 291.09 463.05 Tm 0.19 Tw [( )10(it )10(is fa)4(r more)4( like)4(l)-12(y)20( tha)4(t)-2( )-10(e)4(v)0(e)4(r)-17(y)20( pla)-16(y)20(er in the)]TJ -16.75 -1.67 TD 0 Tw [(population will change strateg)-10(y)20( b)-20(y)20( imitation than even )-10(a sing)10(le pl)-12(a)-16(y)20(er )-10(will innovate.)]TJ 0 -1.66 TD [(B)-13(y)20( wa)-16(y)20( o)-10(f)3( contr)-7(a)4(st standard evolutionar)-17(y)20( mod)-10(e)4(ls of persistent r)-7(a)4(ndomness assume)]TJ /F11 1 Tf 0 -2.17 TD 0.003 Tc -0.003 Tw [(St)6(andar)7(d)-1( M)7(o)3(de)7(l:)]TJ /F8 1 Tf 7.31 0 TD 0 Tc 0 Tw ( )Tj /F9 1 Tf 2.67 0 TD (\020)Tj /F5 1 Tf -2.33 0 TD (#)Tj /F6 1 Tf 1.21 0 TD (\036)Tj /F8 1 Tf 1.87 0 TD (.)Tj /F3 1 Tf -10.73 -2.17 TD -0.001 Tc 0.081 Tw [(Actuall)-13(y)19( th)-11(e standard mod)-11(e)3(l does not use rel)-13(a)3(tive best respons)-12(e for pla)-17(y)19(e)-7(r)2(s who )-10(are )-10(not)]TJ 0 -1.66 TD 0 Tc 0.21 Tw [(innovating)10( )10(\(oft)-12(en )10(called mutatin)-10(g)10(\))3(, but t)-22(y)20(picall)-22(y)20( some va)-6(riation on the best respons)-11(e)]TJ 0 -1.67 TD -0.001 Tc 0.001 Tw [(d)-11(y)19(namic. )-10(As we shall se)-7(e below, this does not make that much di)-13(ffe)-7(renc)-7(e.)]TJ /F1 1 Tf 12 0 2.551 12 90.09 299.01 Tm 0.002 Tc 0 Tw [( D)4(i)0(scus)8(s)-2(ion and )10(Examp)13(l)0(es)]TJ /F3 1 Tf 12 0 0 12 126.09 276.09 Tm -0.001 Tc 0.271 Tw [(W)-7(e)3( )10(should )10(first )10(indicate )10(the strong)9( )-10(conne)-7(ction between the )-10(cas)-12(e of unlikel)-23(y)]TJ -3 -1.67 TD 0.001 Tc [(imita)5(tion )]TJ /F9 1 Tf 6.33 0 TD 0 Tc 0 Tw (\020)Tj /F5 1 Tf -2.33 0 TD (#)Tj /F6 1 Tf 1.21 0 TD (\036)Tj /F3 1 Tf 1.87 0 TD -0.001 Tc 0.061 Tw [(, and the standard )-10(cas)-12(e of innovation \(or mutation\) )-10(and a best-re)-7(sponse)]TJ -7.08 -1.67 TD 0 Tc 0.2 Tw [(like )10(d)-10(y)20(namic. )-10(I)13(n)0( matching )-10(g)10(a)4(mes, )-10(gener)-7(a)4(ll)-12(y)20( sp)-10(eakin)-10(g)10(,)0( the basins of ste)-6(a)4(d)-20(y)20( states a)-6(r)3(e)]TJ 0 -1.66 TD 0.12 Tw [(determined )10(b)-20(y)20( fr)-7(actions of the population. Consequentl)-22(y)20( as the popul)-12(ation siz)-6(e)4( g)10(o)0(es to)]TJ 0 -1.67 TD -0.001 Tc 0.151 Tw [(infinit)-13(y)29(, th)-11(e diffe)-7(ren)-11(ce in the number o)-11(f)2( innovations need)-11(ed to move from one )-10(ste)-7(a)3(d)-21(y)]TJ T* 0.031 Tw [(state to another, ve)-7(rsus the number r)-8(e)3(quired to move b)-11(ack, )-10(t)-23(y)19(picall)-23(y)19( )-20(g)9(o)-1(es )-10(to )-10(infinit)-23(y)19(. )-20(I)12(t)-3( )-10(is)]TJ 0 -1.66 TD -0.002 Tc 0.152 Tw [(t)-4(h)-2(i)-4(s)-3( )10(di)-4(fferenc)-8(e )10(t)-4(h)-2(at)-4( )10(det)-4(e)-8(rm)-4(i)-4(n)-2(es whi)-4(c)2(h a)-8(r)1(e t)-4(h)-2(e st)-4(ocha)-8(st)-4(i)-4(cal)-4(l)-14(y)18( st)-14(ead)-22(y)18( st)-4(at)-4(es. On t)-4(h)-12(e ot)-4(her)]TJ 0 -1.67 TD -0.001 Tc 0.351 Tw [(hand, )10(while the rel)-13(a)3(tive best-r)-8(esponse d)-21(y)19(namic is diff)-8(erent than th)-11(e best-re)-7(sponse)]TJ T* 0 Tc 0.05 Tw [(d)-10(y)20(namic, )10(it )10(r)-7(e)4(quires )10(onl)-22(y)20( )10(a )10(numbe)-6(r of innovations equ)-10(a)4(l to the total number of strate)-6(g)10(i)-12(es)]TJ 0 -1.66 TD 0.002 Tc 0.088 Tw [(in )10(the)6( )10(g)12(a)6(m)-10(e)6( )10(to )10(ma)6(ke)6( sure)6( tha)6(t)0( e)6(v)2(er)-15(y)22( stra)6(teg)-8(y)22( is ac)6(tua)6(l)0(l)-10(y)22( in use)6(.)2( )-20(I)15(n)2( this inte)6(rior c)6(a)6(s)-9(e)6(,)2( the)]TJ 0 -1.67 TD -0.001 Tc 0.211 Tw [(best-response )-10(and rel)-13(a)3(tive best-r)-8(esponse d)-21(y)19(namics a)-7(r)2(e identic)-7(al. Since this )-10(is )-10(a )-10(fix)-11(e)3(d)]TJ ET endstream endobj 60 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F1 36 0 R /F3 38 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F10 61 0 R /F11 62 0 R /T9 63 0 R /T10 64 0 R /T11 65 0 R /T12 66 0 R /T13 67 0 R /T14 68 0 R /T15 69 0 R /T16 70 0 R /T17 71 0 R /T18 72 0 R /T19 73 0 R /T20 74 0 R /T21 75 0 R /T22 76 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 78 0 obj << /Length 7999 >> stream BT /F3 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc 0 Tw (4)Tj -17.75 -3 TD 0.1 Tw [(number of innovations, when the population siz)-6(e)4( is lar)-7(g)10(e )-10(enou)-10(g)10(h, it is swamped b)-20(y)20( the)]TJ 0 -1.66 TD -0.001 Tc 0.151 Tw [(differen)-11(ce )10(in )10(innovations requi)-13(red to move betw)-9(een ste)-7(a)3(d)-21(y)19( states, and the )-10(calculations)]TJ 0 -1.67 TD 0.061 Tw [(made for stoch)-11(a)3(stic stabilit)-13(y)19( in the best-r)-8(esponse case )-10(coincide with )-10(those )-10(in )-10(the )-10(rel)-13(a)3(tive)]TJ T* 0.151 Tw [(best-response )-10(case. )-10(As a r)-8(e)3(sult, ex)-11(cept in knife-ed)-11(g)9(e )-10(cas)-12(es, we do not ex)-11(pect )-10(unlikel)-23(y)]TJ 0 -1.66 TD 0 Tc 0.22 Tw [(imitation )10(to y)30(i)-2(eld diff)-7(erent r)-7(e)4(sults than Kandori, Mailath )-10(and Rob [)-7(1993])-7(, or Young)]TJ 0 -1.67 TD -0.001 Tc 0.001 Tw [([)-8(1993])-8(, or subsequent research usin)-11(g)9( the stand)-11(a)3(rd model.)]TJ 3 -1.67 TD 0 Tc 0.09 Tw [(W)-6(e)4( should also note that the assumption of a sing)10(le-popul)-12(ation is )-10(sig)10(n)0(ificant. )-20(I)13(n)]TJ -3 -1.66 TD 0.04 Tw [(the ex)-10(isting)10( literature, this has been th)-10(e primar)-17(y)20( focus of r)-7(e)4(search, )-10(althoug)10(h Hah)-10(n)0( )-10([)-7(1995])]TJ 0 -1.67 TD 0.28 Tw [(does )10(have some )-10(results in the multiple population case. Her)-7(e)4( the sin)-10(g)10(le-population)]TJ T* 0 Tw [(assumption not onl)-12(y)30( me)-6(ans that all pla)-16(y)20(ers )-10(are )]TJ /F8 1 Tf 18.76 0 TD 0.001 Tc 0.009 Tw (a priori)Tj /F3 1 Tf 3.1 0 TD 0 Tc 0 Tw [( identical, but that )-10(there )-10(is )-10(onl)-12(y)20( )-10(on)-10(e)]TJ -21.86 -1.66 TD -0.001 Tc 0.041 Tw [(population )10(within )10(which )10(ideas spread. Th)-11(e c)-7(a)3(se in which ide)-7(a)3(s ar)-8(e more likel)-23(y)19( to spre)-7(ad)]TJ /F4 1 Tf 0 -1.67 TD 0.011 Tw [(within )10(particular )10(ex)-11(ogenousl)-13(y)19( )10(o)-11(r)2( endo)-11(g)9(e)3(nousl)-23(y)19( identified populations of )-10(\223people like me)-7(\224)]TJ T* 0 Tc 0.24 Tw [(is )10(of )10(g)10(r)-7(eat )10(inter)-7(e)4(st. )10(The )10(model of Friedman [)-7(1998])-7( in which play)20(ers are sometimes)]TJ 0 -1.66 TD 0.02 Tw [(matched with opponents from the s)-11(a)4(me population and sometimes with opponents from a)]TJ 0 -1.67 TD 0.06 Tw [(different population provid)-10(e)4(s a natur)-7(a)4(l setting)10( fo)-10(r this t)-12(y)20(pe o)-10(f)3( )-10(stud)-10(y)20(,)0( )-10(b)-10(u)0(t )-10(it )-10(is )-10(bey)20(ond )-10(the)]TJ T* -0.001 Tc 0.001 Tw [(scope of this pape)-7(r.)]TJ 3 -1.66 TD 0.041 Tw [(A )10(protot)-13(y)19(p)-1(ic)-7(al )10(ex)-11(ample )10(of the t)-13(y)19(p)-11(e)3( of )-10(environment we )-10(are stud)-21(y)19(i)-3(n)-11(g)9( is a )]TJ /F8 1 Tf 29.28 0 TD 0 Tc (matching)Tj -32.28 -1.67 TD -0.001 Tc (game)Tj /F4 1 Tf 2.16 0 TD 0.001 Tc 0.369 Tw [(. )10(A )10(ma)5(tc)5(hin)-9(g)11( g)11(a)5(m)-11(e)5( is de)5(fine)5(d b)-19(y)21( )-10(a)5( utilit)-11(y)31( )-10(func)5(tion )]TJ /T23 1 Tf 8.391 0 0 8.391 426.45 368.85 Tm 1.266 Tc (\021\022)Tj ET q 1 i 416.25 377.97 69.24 -19.92 re W* n BT /F9 1 Tf 12.024 0 0 12.024 416.25 364.05 Tm 0.788 Tc [(\010\014)-209(\014)-239(\014)-349(\011)]TJ ET Q q 1 i 412.17 378.09 73.32 -13.56 re W* n BT /T24 1 Tf 8.391 0 0 8.391 412.41 368.85 Tm 6.804 Tc (J*)Tj ET Q q 1 i 404.49 377.97 81 -19.92 re W* n BT /F5 1 Tf 12.024 0 0 12.024 404.49 364.05 Tm 0.727 Tc [(UA)18(A)-1349(A)]TJ ET Q BT /F10 1 Tf 12.024 0 0 12.024 406.05 364.41 Tm 0 Tc 0 Tw (%)Tj 3.6228 -0.0299 TD (K)Tj /F4 1 Tf 12 0 0 12 485.49 364.05 Tm -0.002 Tc 0.372 Tw [( where)]TJ /F9 1 Tf -30.87 -1.67 TD -0.13 Tc [(\021\014)-230(\022)-50(\014)-1160(\014)]TJ /F5 1 Tf -1.8 0 TD 4.3 Tc (J*)Tj /F6 1 Tf 0.74 0 TD 0 Tc 0 Tw (\036)Tj /F10 1 Tf 2.56 0 TD (K)Tj /F4 1 Tf 2.25 0 TD -0.002 Tc 0.062 Tw [( are pl)-4(a)-18(y)18(e)-8(r)1( rol)-4(e)2(s, )-10(and )]TJ /T25 1 Tf 8.379 0 0 8.379 276.45 348.81 Tm 0 Tc 0 Tw (J)Tj /F5 1 Tf 12 0 0 12 268.65 344.01 Tm 1.781 Tc (A!)Tj /F6 1 Tf 1.34 0 TD 0 Tc (\211)Tj /F4 1 Tf 1.94 0 TD 0.06 Tw [(, a finite set, is called )-10(an )-20(action. )-10(Pla)-6(y)20(e)-6(r)3(s )-10(a)-6(r)3(e)]TJ -18.16 -1.66 TD -0.001 Tc 0.441 Tw [(randoml)-13(y)19( assig)9(n)-11(ed )10(to )10(diffe)-7(rent )10(roles. )10(Strate)-7(g)9(i)-13(es ar)-8(e maps from rol)-13(e)3(s to actions)]TJ /F9 1 Tf 0.94 -1.67 TD 0.27 Tc [(\032[)370(\021)390(\014)180(\022)350(\014)-770(\014)-420(])]TJ /F5 1 Tf -0.78 0 TD 4.139 Tc [(S*)1909(!)]TJ /F6 1 Tf 5.98 0 TD 0 Tc 0 Tw (l)Tj /F10 1 Tf -2.75 0 TD (K)Tj /F4 1 Tf 5.03 0 TD -0.001 Tc 0.051 Tw (. The function )Tj /F9 1 Tf 6.76 0 TD 0.33 Tc [(\010\014)-370(\011)]TJ /F5 1 Tf -0.55 0 TD 0.32 Tc (US)Tj /F7 1 Tf 1.66 0 TD 0 Tc 0 Tw (T)Tj /F4 1 Tf 1.17 0 TD 0.001 Tc 0.049 Tw [( is c)5(o)1(mpute)5(d)1( b)-9(y)21( ca)5(lc)5(ula)5(tin)-9(g)11( the)5( proba)5(bilit)-21(y)21( )-10(of)]TJ -17.46 -1.67 TD 0 Tc 0 Tw [(pla)-6(y)20(in)-10(g)10( diff)-7(erent )-10(roles, and me)-6(eting)10( oppon)-10(ents play)20(i)-12(n)-10(g)10( dif)-7(f)3(er)-7(ent roles.)]TJ /T26 1 Tf 8.363 0 0 8.363 322.17 261.69 Tm 2.879 Tc (\021\022)Tj -10.4605 -1.234 TD 4.4 Tc (\021\\)Tj /F9 1 Tf 11.983 0 0 11.983 137.73 257.01 Tm 0.001 Tc [(\010)-330(\014)-700(\011)-1352(\010)81(\021)-60(\017)-721(\011)-8642(\010)-791(\010)81(\021)80(\011\014)-991(\010)51(\022)30(\011\014)-1031(\014)-1091(\010)-560(\011\011)-3124(\010)-911(\011)]TJ /T27 1 Tf 5.992 0 0 5.992 270.93 254.61 Tm 1.372 Tc (*J)Tj /T28 1 Tf 8.363 0 0 8.363 223.53 264.45 Tm 0 Tc (*)Tj 10.1448 -0.33 TD 10.099 Tc [(J*)1724(K)]TJ 15.2387 -1.2197 TD 1.014 Tc (KJ)Tj -25.24 -0.0143 TD 3.398 Tc [(JS)2627(3)2557(S)2053(S)]TJ /F5 1 Tf 11.983 0 0 11.983 131.13 257.01 Tm 0.321 Tc [(US)-3835(*)-7852(U)-441(S)-1611(S)-3053(S)-580(*)-4036(S)]TJ /F7 1 Tf 1.6624 0 TD 24.646 Tc (TT)Tj /T29 1 Tf 8.363 0 0 8.363 440.73 251.49 Tm 0 Tc (v)Tj -25.3978 -0.0143 TD 3.049 Tc [(\036\211)659(\036)]TJ /F6 1 Tf 11.983 0 0 11.983 166.17 257.01 Tm 0 Tc (\036)Tj 17.974 0 0 17.974 208.29 254.25 Tm 0.955 Tc (\234\234)Tj 11.857 -0.0134 TD 0 Tc (\217)Tj /T30 1 Tf 8.363 0 0 8.363 256.29 251.61 Tm 2.09 Tc (%%)Tj /F10 1 Tf 11.983 0 0 11.983 302.01 257.37 Tm 0.743 Tc [(%%)-1101(%)-2543(%)-4957(%)]TJ 5.9687 -0.03 TD 0 Tc (K)Tj /F4 1 Tf 12 0 0 12 90.09 224.01 Tm -0.001 Tc 0.511 Tw [(W)-7(e)3( )10(make the fairl)-23(y)19( standa)-7(rd, and in a l)-13(a)3(r)-8(g)9(e population r)-8(e)3(lativel)-23(y)19( innocuous,)]TJ 0 -1.66 TD 0.231 Tw [(simplification that a pla)-7(y)19(e)-7(r)2( does not take into )-10(a)-7(ccount )-10(the )-10(f)-8(act )-10(that )-10(he )-20(cannot )-10(me)-7(et)]TJ 0 -1.67 TD 0.001 Tc 0.009 Tw [(himse)5(l)-1(f. Notic)5(e)5( tha)5(t)-1( onl)-11(y)21( in the)5( )-20(c)5(a)5(s)0(e)5( )-10(o)-9(f)4( )-10(two )-10(pla)-15(y)21(er )-10(ga)5(me)5(s )-10(is )]TJ /F9 1 Tf 24.88 0 TD 0.33 Tc [(\010\014)-370(\011)]TJ /F5 1 Tf -0.55 0 TD 0.32 Tc (US)Tj /F7 1 Tf 1.66 0 TD 0 Tc 0 Tw (T)Tj /F4 1 Tf 1.17 0 TD 0.001 Tc 0.019 Tw [( line)5(a)5(r)4( in )]TJ /F7 1 Tf 4.06 0 TD 0 Tc 0 Tw (T)Tj /F4 1 Tf 0.88 0 TD 0.02 Tw (, which is)Tj -32.1 -1.67 TD 0.28 Tw [(the)4( )10(most )10(fa)4(milia)4(r )10(c)4(a)4(s)-1(e)4(.)0( Also of inte)4(re)4(st are)4( )]TJ /F8 1 Tf 19.38 0 TD -0.001 Tc 0.281 Tw [(anony)-7(mous matching games)]TJ /F4 1 Tf 11.89 0 TD -0.002 Tc [( w)-10(h)-2(ich ar)-9(e)]TJ -31.27 -1.66 TD -0.001 Tc 0.031 Tw [(matching)9( )-10(games in which strate)-7(g)9(i)-13(es ar)-8(e restrict)-13(ed to be independ)-11(ent of the pla)-17(y)19(e)-7(r)2( )-10(role, )-10(so)]TJ 0 -1.67 TD 0.001 Tc [(tha)5(t)-1( )]TJ /F5 1 Tf 1.92 0 TD 1.55 Tc (3!)Tj /F6 1 Tf 1.02 0 TD 0 Tc 0 Tw (\036)Tj /F4 1 Tf 2.06 0 TD (.)Tj ET endstream endobj 79 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F3 38 0 R /F4 43 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F10 61 0 R /T23 80 0 R /T24 81 0 R /T25 82 0 R /T26 83 0 R /T27 84 0 R /T28 85 0 R /T29 86 0 R /T30 87 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 88 0 obj << /Length 9312 >> stream BT /F3 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc 0 Tw (5)Tj /F1 1 Tf 14.04 0 0 14.04 90.09 704.01 Tm 0.004 Tw [(3. Bas)9(i)-4(c)9( Result)25(s)]TJ /F3 1 Tf 12 0 0 12 126.09 681.09 Tm 0.001 Tc 0.059 Tw [(We)5( be)5(g)11(i)-1(n b)-19(y)21( e)5(s)0(ta)5(blishin)-9(g)11( some)5( ba)5(sic)5( )-10(re)5(sults. )-10(F)7(i)-1(rst, )-10(we)5( )-20(e)5(x)-9(a)5(mine)5( )-10(the)5( )-10(re)5(la)5(tive)5( )-10(b)-9(e)5(st-)]TJ -3 -1.67 TD -0.001 Tc 0.231 Tw [(response d)-21(y)19(namic in the unp)-11(erturbed )-10(cas)-12(e )]TJ /F9 1 Tf 11.931 0 0 11.931 336.57 661.05 Tm 0 Tc 0 Tw (\020)Tj ET q 1 i 313.29 671.97 24.12 -13.92 re W* n BT /F7 1 Tf 11.931 0 0 11.931 313.29 661.05 Tm (F)Tj ET Q q 1 i 323.01 671.97 22.68 -13.92 re W* n BT /F6 1 Tf 11.931 0 0 11.931 323.01 661.05 Tm (\036)Tj ET Q BT /F3 1 Tf 12 0 0 12 345.69 661.05 Tm 0.001 Tc 0.229 Tw [(. This dy)21(n)-9(a)5(mic)5( is simila)5(r )-10(in )-10(some)]TJ -21.3 -1.67 TD -0.002 Tc 0.082 Tw [(respect)-4(s )10(t)-4(o)-2( )10(t)-4(h)-2(e )10(r)-9(e)2(pl)-4(i)-4(cat)-4(or:)-4( )10(fo)-12(r )10(ex)-12(am)-4(pl)-4(e, al)-4(l)-4( pure profi)-4(l)-14(es ar)-9(e st)-4(ead)-22(y)18( st)-4(at)-4(es, but)-4( poi)-4(nt)-4(s t)-4(h)-2(at)]TJ 0 -1.66 TD -0.001 Tc 0.081 Tw [(are not Nash )-10(equilibria are not locall)-23(y)19( stable. Second, )-10(we establish two basic )-10(results )-10(for)]TJ 0 -1.67 TD -0.002 Tc 0.092 Tw [(the perturbed )-10(case )]TJ /F9 1 Tf 9.9 0 TD 0 Tc 0 Tw (\020)Tj /F7 1 Tf -1.89 0 TD (F)Tj /F6 1 Tf 0.78 0 TD (\037)Tj /F3 1 Tf 1.83 0 TD 0.1 Tw [(. When imitation is much more likel)-12(y)30( th)-10(an innovation, mix)-10(ed)]TJ -10.62 -1.67 TD -0.001 Tc 0.091 Tw [(strate)-7(g)9(i)-3(es should be less stable than pu)-11(re strat)-13(e)-7(g)9(i)-3(es. A )-10(mix)-11(ed )-10(strateg)-11(y)19( )-20(can )-10(evolv)-11(e)3( )-10(into )-10(a)]TJ 0 -1.66 TD 0 Tc 0.04 Tw [(pure strateg)-10(y)20( pu)-10(rel)-22(y)20( throu)-10(g)10(h imitation, while a pure str)-7(a)4(teg)-10(y)20( cannot )-10(evolve )-10(at )-20(all )-10(without)]TJ 0 -1.67 TD 0.18 Tw [(at )10(least )10(one )10(innovation. )10(We )10(confirm )10(this intuition by)20( sho)-10(w)2(ing)10( th)-10(at the limit invariant)]TJ T* 0.001 Tc (distribution )Tj /F7 1 Tf 5.22 0 TD 0 Tc 0 Tw (N)Tj /F3 1 Tf 0.86 0 TD -0.001 Tc 0.141 Tw [( pl)-3(aces w)-9(e)3(i)-3(g)9(ht)-3( onl)-23(y)19( on pur)-8(e profi)-3(l)-3(e)3(s i)-3(n)-1( )]TJ /F5 1 Tf 9.38 0 0 9.38 374.37 526.77 Tm 0 Tc 0 Tw (M)Tj /F6 1 Tf 13.44 0 0 13.44 366.09 521.37 Tm (4)Tj /F3 1 Tf 12 0 0 12 384.57 521.01 Tm -0.001 Tc 0.151 Tw [(. W)-7(e)3( then further stud)-21(y)19( the)]TJ -24.54 -1.66 TD 0.001 Tc 0.159 Tw [(c)5(onne)5(c)5(tion be)5(tw)-7(e)5(e)5(n)1( the)5( limit inva)5(ria)5(n)1(t distribution )]TJ /F7 1 Tf 21.68 0 TD 0 Tc 0 Tw (N)Tj /F3 1 Tf 0.86 0 TD 0.17 Tw [( )10(a)4(nd Na)4(sh e)4(quilibrium, showing)]TJ -22.54 -1.67 TD 0 Tw (that if the support of )Tj /F7 1 Tf 8.64 0 TD (N)Tj /F3 1 Tf 0.86 0 TD [( is a sing)10(leton, it must be a Nash equilibrium.)]TJ -6.5 -1.67 TD -0.011 Tc [(Le)-7(t)-13( )]TJ /T31 1 Tf 8.391 0 0 8.391 156.57 465.81 Tm 0 Tc (\020)Tj /F7 1 Tf 12.024 0 0 12.024 149.01 461.01 Tm (N)Tj /F3 1 Tf 12 0 0 12 164.37 461.01 Tm 0.11 Tw [( be an irr)-7(e)4(ducible inva)-6(riant distribution of the Markov )-10(pro)-10(cess )-10(in )-10(which)]TJ /F9 1 Tf 11.931 0 0 11.931 116.01 441.09 Tm 0 Tw (\020)Tj /F7 1 Tf -1.9512 0 TD (F)Tj /F6 1 Tf 0.8147 0 TD (\036)Tj /F3 1 Tf 12 0 0 12 125.13 441.09 Tm 0.001 Tc 0.109 Tw [(. L)22(e)5(t )]TJ /F7 1 Tf 2.5 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.002 Tc 0.102 Tw [( be t)-4(h)-2(e set)-4( of m)-4(i)-4(x)-12(ed st)-4(rat)-4(e)-8(g)8(i)-4(es i)-4(n)-2( t)-4(h)-2(e st)-4(at)-4(e )-10(spac)-8(e )]TJ /T32 1 Tf 8.379 0 0 8.379 420.81 445.89 Tm 0 Tc 0 Tw (M)Tj /F6 1 Tf 12 0 0 12 412.41 441.09 Tm (4)Tj /F3 1 Tf 1.56 0 TD 0.001 Tc 0.109 Tw [( tha)5(t)-1( this inva)5(ria)5(n)1(t)]TJ -28.42 -1.67 TD 0.009 Tw [(distribution g)11(i)-1(ve)5(s positive)5( we)5(ig)11(ht to. We)5( c)5(a)5(ll suc)5(h)1( a)5(n)1( )]TJ /F7 1 Tf 21.8 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.002 Tc 0.012 Tw [( an )]TJ /F8 1 Tf 1.46 0 TD -0.001 Tc [(ergodi)-13(c set)]TJ /F3 1 Tf 4.43 0 TD 0.001 Tc 0.029 Tw [(. L)12(e)5(t )]TJ /F6 1 Tf 2.32 0 TD 0 Tc 0 Tw (8)Tj /F3 1 Tf 0.97 0 TD -0.002 Tc 0.022 Tw [( be the set)]TJ -31.92 -1.67 TD 0.001 Tc 0.039 Tw [(of a)5(ll suc)5(h)1( )]TJ /F7 1 Tf 4.76 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD 0.001 Tc 0.039 Tw [(. Note)5( tha)5(t)-1( this is a)5( se)5(t )-10(of )-10(se)5(ts. )-20(L)22(e)5(t )]TJ /F9 1 Tf 15.59 0 TD 0.56 Tc (\010\011)Tj /F5 1 Tf -0.63 0 TD 0 Tc 0 Tw (3)Tj /F7 1 Tf 0.98 0 TD (T)Tj /F3 1 Tf 1.18 0 TD -0.001 Tc 0.051 Tw [( d)-11(e)3(note the set of pure strat)-13(e)-7(g)9(i)-3(es)]TJ -22.82 -1.66 TD 0.001 Tc -0.001 Tw [(use)5(d)1( with positive)5( proba)5(bilit)-11(y)21( in )]TJ /F7 1 Tf 13.39 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 0.88 0 TD -0.001 Tc 0.001 Tw [(. F)5(i)-3(rst we )-10(establish some basic f)-8(acts about )]TJ /F6 1 Tf 17.22 0 TD 0 Tc 0 Tw (8)Tj /F3 1 Tf 0.97 0 TD (.)Tj /F11 1 Tf -32.46 -2.17 TD -0.001 Tc 0.151 Tw [(Lemma 3.1:)]TJ /F8 1 Tf 5.25 0 TD 0.002 Tc 0.148 Tw [( The)6( )-10(se)6(ts )]TJ /F7 1 Tf 4.45 0 TD 0 Tc 0 Tw (X)Tj /F8 1 Tf 0.94 0 TD 0.001 Tc 0.159 Tw [( are)5( disjoint. Eac)5(h)1( se)5(t c)5(onsisting of a single)5(t)-1(on pure)5( profile)]TJ /F9 1 Tf -10.47 -1.67 TD 0.35 Tc ([])Tj /F5 1 Tf 0.41 0 TD 0 Tc 0 Tw (S)Tj /F6 1 Tf 1.22 0 TD 0.278 Tc (\2118)Tj /F8 1 Tf 1.87 0 TD 0 Tc (. If )Tj /F9 1 Tf 2.11 0 TD 0.86 Tc (\014\007)Tj /F7 1 Tf -0.55 0 TD 0.369 Tc [(TT)-1300(X)]TJ /F6 1 Tf 2.19 0 TD 1.298 Tc [(\211\211)1020(8)]TJ /F8 1 Tf 3.86 0 TD 0.001 Tc -0.001 Tw [( the)5(n)1( )]TJ /F9 1 Tf 3.02 0 TD 0.56 Tc [(\010\011)-1430(\010)-150(\007)550(\011)]TJ /F5 1 Tf -0.63 0 TD 2.77 Tc (33)Tj /F7 1 Tf 0.99 0 TD 2.749 Tc (TT)Tj /F6 1 Tf 1.26 0 TD 0 Tc 0 Tw (\036)Tj /F8 1 Tf 3.58 0 TD (.)Tj -19.5 -2.16 TD (Proof:)Tj /F3 1 Tf 2.61 0 TD -0.001 Tc 0.001 Tw [( W)-7(h)-1(en )]TJ /F9 1 Tf 11.931 0 0 11.931 185.01 309.09 Tm 0 Tc 0 Tw (\020)Tj /F7 1 Tf -1.9512 0 TD (F)Tj /F6 1 Tf 0.8147 0 TD (\036)Tj /F3 1 Tf 12 0 0 12 194.13 309.09 Tm -0.002 Tc 0.002 Tw ( we have the )Tj /F8 1 Tf 5.26 0 TD -0.001 Tc 0.001 Tw [(r)-12(e)3(lative best-r)-12(esponse dynami)-13(c)]TJ /F3 1 Tf 12.45 0 TD 0.002 Tc 0.008 Tw [( in whic)6(h in e)6(a)-4(c)6(h)2( play)22(er)]TJ -26.38 -1.67 TD 0 Tc 0.15 Tw [(one )10(pla)-16(y)20(er )10(switch)-10(e)4(s with equal prob)-10(abilit)-12(y)20( to one of th)-10(e relative best-respons)-11(es to the)]TJ T* -0.002 Tc 0.032 Tw [(current)-4( st)-4(at)-4(e. )-10(The set)-4(s)-3( )]TJ /F7 1 Tf 9.31 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.001 Tc 0.031 Tw [( are b)-21(y)19( de)-7(finition minimal invariant sets under the relative )-10(b)-11(e)3(st-)]TJ -10.25 -1.66 TD 0 Tc 0.18 Tw [(response d)-20(y)20(namic. Th)-10(at these sets are disjoint is immediate from the )-10(definition. )-10(Pure)]TJ 0 -1.67 TD 0 Tw [(profiles ar)-7(e absorbin)-10(g)10( since no str)-7(a)4(te)-6(g)-10(y)20( c)-6(a)4(n be us)-11(ed unless it is alread)-20(y)20( )-10(in )-10(use. )-10(This )-10(me)-6(ans)]TJ T* -0.003 Tc 0.293 Tw [(t)-5(h)-3(at)-5( ever)-20(y)17( set)-5( )]TJ /F7 1 Tf 6.67 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD 0.29 Tw [( c)4(onsisting)10( of a)4( sin)-10(g)10(le)4( pu)-10(re)4( )-10(stra)4(t)-12(e)-6(g)-10(y)20( )-10(is )-10(in )]TJ /F6 1 Tf 19.2 0 TD 0 Tw (8)Tj /F3 1 Tf 0.97 0 TD -0.002 Tc 0.302 Tw [(. To see t)-4(h)-2(at)-4( hav)-12(e)]TJ /F9 1 Tf -26.98 -1.66 TD 0.56 Tc [(\010\011)-1430(\010)-150(\007)550(\011)]TJ /F5 1 Tf -0.63 0 TD 2.77 Tc (33)Tj /F7 1 Tf 0.99 0 TD 2.749 Tc (TT)Tj /F6 1 Tf 1.26 0 TD 0 Tc 0 Tw (\036)Tj /F3 1 Tf 3.58 0 TD -0.001 Tc 0.071 Tw [(, )10(observe )10(that )10(the )10(r)-8(e)3(lative best-r)-8(esponse d)-21(y)19(n)-11(a)3(mic cannot )-10(ever in)-11(cre)-7(a)3(se the)]TJ -6 -1.67 TD 0.001 Tc 0.089 Tw [(se)5(t of stra)5(teg)11(i)-1(e)5(s)0( in use)5(.)1( )-10(I)14(f)-6( the)5(r)-6(e)5( is a)5( point )]TJ /F9 1 Tf 19.83 0 TD 0.56 Tc [(\010\011)560(\014)-1910(\010)-160(\007)550(\011)]TJ /F5 1 Tf -2.36 0 TD 1.319 Tc [(S3)-431(S)-50(3)]TJ /F7 1 Tf 2.72 0 TD 3.519 Tc (TT)Tj /F6 1 Tf -1.93 0 TD 3.378 Tc (\211\212)Tj /F3 1 Tf 7.55 0 TD 0.001 Tc [( the)5(n)1( the)5( proba)5(bilit)-21(y)21( tha)5(t)]TJ -25.81 -1.67 TD -0.001 Tc 0.001 Tw [(the best-respons)-12(e d)-21(y)19(namic )-10(g)9(o)-1(es f)-8(r)2(om )]TJ /F7 1 Tf 15.34 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 0.88 0 TD 0.001 Tc -0.001 Tw ( to )Tj /F9 1 Tf 2.23 0 TD 0 Tc 0 Tw (\007)Tj /F7 1 Tf -0.76 0 TD (T)Tj /F3 1 Tf 1.22 0 TD 0.001 Tc -0.001 Tw [( is ze)5(ro, )-10(whic)5(h )-10(is )-10(inc)5(onsiste)5(nt )-10(with )-10(the)5( )-10(two)]TJ -18.91 -1.66 TD [(stra)5(teg)11(i)-1(e)5(s)0( l)-11(y)21(in)-9(g)11( in the)5( s)-10(a)5(me)5( e)5(r)-6(g)11(odi)-11(c)5( se)5(t.)]TJ /F12 1 Tf 35.11 -1.67 TD 0 Tc 0 Tw (\346)Tj ET endstream endobj 89 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F1 36 0 R /F3 38 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F11 62 0 R /F12 90 0 R /T31 91 0 R /T32 92 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 94 0 obj << /Length 11006 >> stream BT /F3 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc 0 Tw (6)Tj -14.75 -3 TD 0.03 Tw [(The)4( third pa)4(rt of the)4( )-10(L)11(e)-6(mma)4( me)4(a)4(n)0(s tha)4(t)-2( )-10(for ea)4(c)4(h)0( )]TJ /F7 1 Tf 11.97 0 0 11.97 368.25 704.01 Tm 0 Tw (X)Tj /F6 1 Tf 0.9825 0 TD 0.28 Tc (\2118)Tj /F3 1 Tf 12 0 0 12 402.57 704.01 Tm -0.001 Tc 0.031 Tw [( we ma)-17(y)19( assi)-13(g)9(n)-1( )-10(a )-10(unique)]TJ -26.04 -1.66 TD 0.001 Tw [(set of pure str)-8(a)3(te)-7(g)9(i)-3(es )]TJ /F9 1 Tf 9.3 0 TD 0.63 Tc (\010\011)Tj /F5 1 Tf -0.63 0 TD 0 Tc 0 Tw (3)Tj /F7 1 Tf 1 0 TD (X)Tj /F3 1 Tf 1.25 0 TD -0.001 Tc 0.001 Tw [( correspondin)-11(g)9( to )]TJ /F9 1 Tf 8.05 0 TD 0.56 Tc [(\010\011)560(\014)]TJ /F5 1 Tf -0.63 0 TD 0 Tc 0 Tw (3)Tj ET q 1 i 322.05 696.09 50.04 -18 re W* n BT /F7 1 Tf 12 0 0 12 322.05 684.09 Tm 0.799 Tc [(TT)-550(X)]TJ ET Q BT /F6 1 Tf 12 0 0 12 349.77 684.09 Tm (\211)Tj /F3 1 Tf 1.86 0 TD (.)Tj -20.5 -1.67 TD 0.3 Tw [(The relative b)-10(e)4(st-response d)-20(y)20(namic is similar to the better-kno)-10(wn )-10(replicator)]TJ -3 -1.67 TD -0.001 Tc 0.271 Tw [(d)-11(y)19(namic in sev)-11(e)3(r)-8(a)3(l respec)-7(ts. )-10(L)20(i)-3(k)-11(e)3( the r)-8(e)3(plicator )-10(d)-21(y)19(namic, )-10(th)-11(e )-10(relative )-10(b)-11(e)3(st-respons)-12(e)]TJ 0 -1.66 TD 0.031 Tw [(d)-11(y)19(nam)-3(i)-3(c)3( )10(i)-3(s)-2( )10(abso)-11(rbed b)-21(y)19( pur)-8(e st)-3(rat)-3(e)-7(g)9(i)-13(es and so has m)-3(a)3(n)-21(y)19( st)-3(e)-7(a)3(d)-21(y)19( st)-3(at)-3(es. How)-9(e)3(ve)-7(r, as i)-3(s)-2( t)-3(h)-1(e)]TJ 0 -1.67 TD -0.002 Tc 0.242 Tw [(case )10(wi)-4(t)-4(h)-2( )10(t)-4(h)-2(e )10(r)-9(e)2(pl)-4(i)-4(cat)-4(or, )10(t)-4(h)-2(i)-4(s)-3( i)-4(s)-3( offset)-4( som)-4(e)2(wh)-12(at)-4( b)-22(y)18( t)-4(h)-2(e fa)-8(ct)-4( t)-4(h)-2(at)-4( poi)-4(nt)-4(s t)-4(h)-2(at)-4( do not)]TJ T* 0 Tc 0.17 Tw [(correspond to N)-8(a)4(sh equilibria are locall)-12(y)20( unstable. B)-13(y)20( )-10(locall)-12(y)20( unstabl)-12(e, )-10(we )-10(mean )-10(that)]TJ 0 -1.66 TD -0.001 Tc 0.041 Tw [(there )10(is )10(a nei)-13(g)9(hborhood of)-8( the state )-10(and a ch)-11(an)-11(g)9(e)3( in strat)-13(e)-7(g)-11(y)19( b)-21(y)19( a sin)-11(g)9(le pla)-17(y)19(e)-7(r)2( that leads)]TJ 0 -1.67 TD 0 Tc 0 Tw [(to a positive probabilit)-12(y)20( of ex)-10(iting)10( that nei)-12(g)10(hborhood.)]TJ /F11 1 Tf 0 -2.17 TD -0.001 Tc 0.451 Tw [(Theore)-7(m)12( 3.2:)]TJ /F8 1 Tf 6.16 0 TD [( Suppose )]TJ /F7 1 Tf 4.94 0 TD 0 Tc 0 Tw (T)Tj /F8 1 Tf 0.88 0 TD 0.45 Tw [( is such that for some )]TJ /F5 1 Tf 11.931 0 0 11.931 373.53 518.01 Tm 0 Tw (S)Tj /F10 1 Tf 0.0704 0.0302 TD (%)Tj /F8 1 Tf 12 0 0 12 382.65 518.01 Tm 0.002 Tc 0.448 Tw [( with )]TJ /F9 1 Tf 3.9 0 TD 0.42 Tc [(\010\011)-940(\020)]TJ /F5 1 Tf 0.31 0 TD 0 Tc 0 Tw (S)Tj /F7 1 Tf -0.88 0 TD (T)Tj /F6 1 Tf 2.03 0 TD (\037)Tj /F10 1 Tf -1.08 0.03 TD (%)Tj /F8 1 Tf 2.93 -0.03 TD -0.001 Tc 0.461 Tw [( we have)]TJ /F9 1 Tf -30.87 -1.66 TD 0.33 Tc [(\010\014)-370(\011)-1530(\010)-60(\014)-370(\011)]TJ /F5 1 Tf -0.55 0 TD 0.32 Tc [(US)-2369(U)10(S)]TJ /F7 1 Tf 1.66 0 TD 3.439 Tc (TT)Tj /F6 1 Tf 1.23 0 TD 0 Tc 0 Tw (\037)Tj /F10 1 Tf 2 0.03 TD (%)Tj /F3 1 Tf 1.94 -0.03 TD (.)Tj /F8 1 Tf 0.25 0 TD 0.001 Tc -0.001 Tw [( The)5(n)1( for all suffic)5(ie)5(ntly)5( large)5( )]TJ /F5 1 Tf 12.39 0 TD 0 Tc 0 Tw (N)Tj /F8 1 Tf 0.91 0 TD 0.001 Tc -0.001 Tw (, if )Tj ET q 1 i 354.81 508.05 33.6 -13.92 re W* n BT /F7 1 Tf 11.931 0 0 11.931 354.81 498.09 Tm 1.37 Tc (TX)Tj ET Q BT /F6 1 Tf 11.931 0 0 11.931 366.09 498.09 Tm 0 Tc 0 Tw (\211)Tj /F8 1 Tf 12 0 0 12 388.41 498.09 Tm 0.001 Tc -0.001 Tw [( it is loc)5(a)1(lly)5( unstable)5(.)]TJ -24.86 -2.17 TD 0 Tc (Proof:)Tj /F3 1 Tf 2.61 0 TD -0.003 Tc 0.043 Tw [( S)-7(i)-5(nce )]TJ /F5 1 Tf 2.97 0 TD 0 Tc 0 Tw (U)Tj /F3 1 Tf 0.83 0 TD -0.001 Tc 0.041 Tw [( is continuous, there is a nei)-13(g)9(hborhood o)-11(f)2( )]TJ /F7 1 Tf 17.34 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 0.88 0 TD 0.001 Tc 0.049 Tw [( in whic)5(h )]TJ /F9 1 Tf 4.84 0 TD 0.33 Tc [(\010\014)-370(\011)-1530(\010)-60(\014)-370(\011)]TJ /F5 1 Tf -0.55 0 TD 0.32 Tc [(US)-2369(U)10(S)]TJ /F7 1 Tf 1.66 0 TD 3.439 Tc (TT)Tj /F6 1 Tf 1.23 0 TD 0 Tc 0 Tw (\037)Tj /F10 1 Tf 2 0.03 TD (%)Tj /F3 1 Tf 1.94 -0.03 TD (.)Tj -35.75 -1.67 TD -0.001 Tc 0.031 Tw (Also, since )Tj /F9 1 Tf 5.52 0 TD 0.42 Tc [(\010\011)-940(\020)]TJ /F5 1 Tf 0.31 0 TD 0 Tc 0 Tw (S)Tj /F7 1 Tf -0.88 0 TD (T)Tj /F6 1 Tf 2.03 0 TD (\037)Tj /F10 1 Tf -1.08 0.03 TD (%)Tj /F3 1 Tf 2.93 -0.03 TD 0.04 Tw [( )10(we ma)-16(y)20( )-10(assume that this is also the case in this nei)-12(g)10(hborhood. )-10(F)6(o)0(r)]TJ /F5 1 Tf -8.66 -1.66 TD 0 Tw (N)Tj /F3 1 Tf 0.91 0 TD 0.01 Tw [( sufficientl)-12(y)20( l)-12(a)4(r)-7(g)10(e th)-10(e neighborhood must contain points in )-10(which )-10(one )-10(pla)-16(y)20(e)-6(r)3( )-10(is )-10(pla)-16(y)20(in)-10(g)]TJ /F5 1 Tf -0.92 -1.67 TD 0 Tw (S)Tj /F3 1 Tf 0.76 0 TD -0.001 Tc 0.231 Tw [(. At each such)-11( point, the relative best-r)-8(esponse )-10(assig)9(n)-1(s positive prob)-11(abilit)-13(y)19( to the)]TJ -0.92 -1.67 TD 0 Tc 0 Tw [(number of )-10(pla)-16(y)20(e)-6(r)3(s )-10(pla)-16(y)20(ing )]TJ /F5 1 Tf 11.931 0 0 11.931 221.73 392.01 Tm (S)Tj /F10 1 Tf 0.0704 0.0302 TD (%)Tj /F3 1 Tf 12 0 0 12 230.85 392.01 Tm 0.001 Tc 0.009 Tw [( de)5(c)5(r)4(e)5(a)5(s)0(in)-9(g)11( b)-19(y)21( on)-9(e)5(,)1( so the)5(r)4(e)5( is positive)5( proba)5(bility)21( )-10(of e)5(x)-9(iting)]TJ -11.73 -1.66 TD -0.001 Tc 0.001 Tw [(the neig)9(hbo)-11(rhood.)]TJ /F12 1 Tf 35.11 -1.67 TD 0 Tc 0 Tw (\346)Tj /F3 1 Tf -32.11 -1.67 TD -0.002 Tc 0.002 Tw [(Turni)-4(n)-2(g)8( t)-4(o)-2( t)-4(h)-2(e )-10(case )]TJ /F9 1 Tf 10.05 0 TD 0 Tc 0 Tw (\020)Tj /F7 1 Tf -1.89 0 TD (F)Tj /F6 1 Tf 0.78 0 TD (\037)Tj /F3 1 Tf 1.83 0 TD -0.001 Tc 0.001 Tw [(, from a theo)-11(rem of Youn)-11(g)9( [)-8(1993])-8( )]TJ /F7 1 Tf 14.11 0 TD 0 Tc 0 Tw (N)Tj /F3 1 Tf 0.86 0 TD 0.01 Tc -0.01 Tw [( m)8(a)-6(y)30( b)10(e)14( )-10(de)14(s)9(c)14(r)13(i)8(be)14(d)]TJ -28.74 -1.66 TD 0 Tc 0.01 Tw [(a)4(s)-1( a)4( proba)4(bilit)-22(y)20( distribution ove)4(r )]TJ /F6 1 Tf 13.54 0 TD 0 Tw (8)Tj /F3 1 Tf 0.97 0 TD 0.001 Tc 0.009 Tw [(. Our intuition tha)5(t)-1( pure)5( stra)5(teg)11(i)-1(e)5(s)0( )-10(a)5(r)4(e)5( more)5( importa)5(nt)]TJ -14.51 -1.67 TD 0 Tc 0 Tw [(in a setting)10( of innovation is confirm)-12(e)4(d b)-20(y)20( our first theo)-10(rem.)]TJ /F11 1 Tf 0 -2.17 TD -0.001 Tc 0.141 Tw [(Theore)-7(m)12( 3.3:)]TJ /F8 1 Tf 5.85 0 TD 0 Tc 0.15 Tw [( )-10(W)13(ith unlikel)-12(y innovation the limit invariant distribut)8(ion )]TJ /F7 1 Tf 24.15 0 TD 0 Tw (N)Tj /F8 1 Tf 0.86 0 TD 0.15 Tw [( puts weight)]TJ -30.86 -1.66 TD -0.001 Tc 0.001 Tw (only on the sets )Tj /F7 1 Tf 11.97 0 0 11.97 170.01 246.09 Tm 0 Tc 0 Tw (X)Tj /F6 1 Tf 0.9825 0 TD 0.28 Tc (\2118)Tj /F8 1 Tf 12 0 0 12 204.33 246.09 Tm 0 Tc ( that consist of a single pure strategy .)Tj 8.04 0 0 8.04 388.05 251.61 Tm (3)Tj /F3 1 Tf 12 0 0 12 126.09 220.05 Tm 0.03 Tw [(To )10(prove)4( )10(this the)4(o)0(re)4(m, a)4(nd ou)-10(r a)4(dditiona)4(l re)4(sults, we)4( )-10(will use)4( the)4( c)4(h)0(a)4(r)-7(a)4(c)4(t)-2(eriza)4(tion)]TJ -3 -1.67 TD -0.002 Tc (of )Tj /F7 1 Tf 1.3 0 TD 0 Tc 0 Tw (N)Tj /F3 1 Tf 0.86 0 TD [( g)10(i)-2(ven )-10(b)-20(y)20( Youn)-10(g)10( [)-7(1993])-7(.)]TJ 8.04 0 0 8.04 234.33 205.53 Tm (4)Tj 12 0 0 12 238.41 200.01 Tm -0.011 Tc 0.021 Tw [( Le)-7(t)-13( )]TJ /F7 1 Tf 2.06 0 TD 0 Tc 0 Tw (U)Tj /F3 1 Tf 0.78 0 TD -0.002 Tc 0.002 Tw [( be a tree )-10(whose nodes ar)-9(e the s)-13(e)2(t )]TJ /F6 1 Tf 13.77 0 TD 0 Tc 0 Tw (8)Tj /F3 1 Tf 0.97 0 TD -0.001 Tc 0.001 Tw [(. W)-7(e)3( )-10(denote )-10(b)-11(y)]TJ /F9 1 Tf -29.22 -1.66 TD 0.62 Tc (\010\011)Tj /F7 1 Tf -0.5 0 TD 0.39 Tc (UX)Tj /F3 1 Tf 2.11 0 TD -0.001 Tc 0.061 Tw [( the unique prede)-7(cessor of)-8( )]TJ /F7 1 Tf 11.27 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.001 Tc 0.061 Tw (. An )Tj /F7 1 Tf 2.32 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.002 Tc 0.072 Tw [(-t)-4(ree )10(i)-4(s)-3( a t)-4(r)-9(ee whose)-8( root)-4( i)-4(s)-3( )]TJ /F7 1 Tf 11.72 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.002 Tc 0.072 Tw [(. F)4(o)-2(r an)-22(y)18( )-10(two)]TJ -30.46 -1.67 TD 0.001 Tc (points )Tj /F9 1 Tf 3.52 0 TD 0 Tc 0 Tw (\014)Tj /F7 1 Tf -0.59 0 TD 0.38 Tc (XX)Tj /F6 1 Tf 1.98 0 TD 0.278 Tc (\2118)Tj /F10 1 Tf -0.85 0.02 TD 0 Tc (%)Tj /F3 1 Tf 2.73 -0.02 TD -0.002 Tc 0.012 Tw [( we defi)-4(ne )-10(t)-4(h)-2(e )-10(r)-9(e)2(si)-4(st)-4(ance )]TJ /F9 1 Tf 10.79 0 TD 0.58 Tc [(\010\014)-190(\011)]TJ /F5 1 Tf -0.47 0 TD 0 Tc 0 Tw (R)Tj /F7 1 Tf 0.85 0 TD 0.38 Tc (XX)Tj ET q 1 i 319.17 172.05 13.2 -18 re W* n BT /F10 1 Tf 12 0 0 12 319.17 160.29 Tm 0 Tc (%)Tj ET Q BT /F3 1 Tf 12 0 0 12 332.37 160.05 Tm 0 Tc 0.02 Tw [( a)4(s)-1( follows. F)6(i)-2(rst, )-10(a)4( pa)4(th from )]TJ /F7 1 Tf 12.39 0 TD 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD 0.001 Tc 0.019 Tw [( to )]TJ /F7 1 Tf 11.931 0 0 11.931 510.81 160.05 Tm 0 Tc 0 Tw (X)Tj /F10 1 Tf 0.1307 0.0101 TD (%)Tj /F3 1 Tf 12 0 0 12 90.09 133.53 Tm ( )Tj ET 1 i 90.09 136.65 143.88 -0.48 re f BT 6.48 0 0 6.48 90.09 125.01 Tm (3)Tj 9.96 0 0 9.96 93.33 120.45 Tm 0.005 Tc 0.191 Tw [( A)16( s)8(i)-6(m)12(i)-6(l)6(a)3(r res)8(u)11(l)6(t)6( )-12(h)11(a)3(s)8( been)11( )-12(s)8(h)11(own f)13(o)-1(r im)12(i)6(t)6(a)3(t)6(i)6(o)-13(n)11( i)6(n)11( th)11(e )-12(f)13(o)-1(r)-11(m)24( of)13( gen)11(e)3(t)6(i)6(c)3( )-12(alg)11(o)-1(ri)6(thm)12(s)8(. )-12(S)7(ee )-12(Da)-9(w)16(i)6(d )-12([1999])]TJ -0.3253 -1.1566 TD 0.004 Tc -0.001 Tw [(T)-12(h)10(eorem)23( 4.2.1, f)12(o)-2(r ex)10(am)23(pl)5(e.)]TJ 6.48 0 0 6.48 90.09 102.09 Tm 0 Tc 0 Tw (4)Tj 9.96 0 0 9.96 93.33 97.53 Tm 0.005 Tc 0.034 Tw [( )12(A)16(l)6(th)11(ough)11( )12(t)6(h)11(e s)8(t)6(an)11(dard )12(con)11(v)11(e)-9(n)11(t)6(i)6(o)-13(n)11( )12(i)6(n)11( )-12(g)11(a)-9(m)12(e)3( t)6(h)11(eor)-11(y)23( is)8( t)6(h)11(a)-9(t)6( a t)6(r)1(ee beg)11(i)6(ns)8( at)6( t)6(h)11(e root)6(, You)11(n)-1(g)11( [1993] f)13(o)-1(l)6(l)6(o)-1(w)28(e)3(d)]TJ -0.3253 -1.1566 TD -0.002 Tc 0.065 Tw [(the )-12(m)17(a)-16(the)-16(m)5(atica)-16(l)-1( co)-8(nve)-16(ntio)-20(n that i)-13(t)-1( end)-8(s)1( t)-13(h)4(ere. W)-10(e)-4( have )-12(used)-8( the )-12(us)-11(ual )-12(ga)-16(m)17(e)-16(-)6(t)-1(h)-8(e)-4(o)-8(r)-6(etic co)-8(n)-8(v)4(entio)-20(n, so)-8( )-12(o)-8(u)4(r)]TJ /F4 1 Tf T* 0.004 Tc -0.001 Tw [(t)5(r)0(ees)7( g)10(o)-2( t)5(h)10(e oppos)7(i)5(t)5(e)2( di)5(rect)5(i)5(o)-2(n)10( of)12( Youn)10(g\222s)7(.)]TJ ET endstream endobj 95 0 obj << /ProcSet [/PDF /Text ] /Font << /F3 38 0 R /F4 43 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F10 61 0 R /F11 62 0 R /F12 90 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 97 0 obj << /Length 15327 >> stream BT /F3 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc 0 Tw (7)Tj -17.75 -3 TD -0.001 Tc 0.091 Tw [(is a sequenc)-7(e )-10(of )-10(points )]TJ /T33 1 Tf 8.391 0 0 8.391 220.65 700.17 Tm 0 Tc 0 Tw (\020)Tj /F9 1 Tf 12.024 0 0 12.024 209.37 704.01 Tm 0.907 Tc [(\010\014)-120(\014)-450(\011)]TJ /T34 1 Tf 8.391 0 0 8.391 289.41 708.81 Tm 0 Tc (M)Tj -4.4478 -1.0583 TD (+)Tj /F7 1 Tf 12.024 0 0 12.024 213.69 704.01 Tm 2.064 Tc (TT)Tj /F6 1 Tf 4.541 0 TD 0.276 Tc (\2074)Tj /F10 1 Tf -3.2735 0 TD 0 Tc (K)Tj /F3 1 Tf 12 0 0 12 300.45 704.01 Tm 0.001 Tc (with )Tj ET q 1 i 335.37 710.01 16.8 -12.96 re W* n BT /T35 1 Tf 8.391 0 0 8.391 335.37 700.29 Tm 0 Tc (\020)Tj ET Q BT /F7 1 Tf 12.028 0 0 12.028 328.41 704.01 Tm 1.744 Tc (TX)Tj /F6 1 Tf 1.3369 0 TD 0 Tc (\211)Tj /F3 1 Tf 12 0 0 12 367.05 704.01 Tm (, )Tj /T36 1 Tf 8.355 0 0 8.355 383.37 699.81 Tm (+)Tj /F7 1 Tf 11.975 0 0 11.975 376.65 703.89 Tm 2.035 Tc (TX)Tj /F6 1 Tf 1.6234 0 TD 0 Tc (\211)Tj /F10 1 Tf 1.1123 0.02 TD (%)Tj /F3 1 Tf 12 0 0 12 419.25 704.01 Tm -0.001 Tc 0.101 Tw [( and )]TJ /T37 1 Tf 8.391 0 0 8.391 465.45 699.93 Tm 0 Tc 0 Tw (\021)Tj /T38 1 Tf -1.3587 0 TD (K)Tj /F7 1 Tf 12.028 0 0 12.028 447.45 704.01 Tm (T)Tj /T39 1 Tf 8.391 0 0 8.391 459.09 699.93 Tm (\014)Tj /F3 1 Tf 12 0 0 12 472.05 704.01 Tm -0.003 Tc 0.103 Tw [( reachabl)-15(e)]TJ -31.83 -1.66 TD 0 Tc (from )Tj /T40 1 Tf 8.391 0 0 8.391 127.53 680.01 Tm 0 Tw (K)Tj /F7 1 Tf 12.028 0 0 12.028 120.93 684.09 Tm (T)Tj /F3 1 Tf 12 0 0 12 135.57 684.09 Tm -0.002 Tc 0.192 Tw [( )10(b)-12(y)18( a si)-4(n)-12(g)8(l)-4(e)2( pl)-4(a)-18(y)18(e)-8(r)1( chan)-12(g)8(i)-4(n)-12(g)8( st)-4(r)-9(a)2(t)-4(e)-8(g)-12(y)18(. )-10(I)11(f)1( t)-4(h)-12(e chan)-12(ge from)-4( )]TJ /T40 1 Tf 8.391 0 0 8.391 443.37 680.01 Tm 0 Tc 0 Tw (K)Tj /F7 1 Tf 12.028 0 0 12.028 436.77 684.09 Tm (T)Tj /F3 1 Tf 12 0 0 12 451.41 684.09 Tm 0.001 Tc 0.189 Tw [( to )]TJ /T37 1 Tf 8.391 0 0 8.391 491.61 680.01 Tm 0 Tc 0 Tw (\021)Tj /T40 1 Tf -1.3587 0 TD (K)Tj /F7 1 Tf 12.028 0 0 12.028 473.61 684.09 Tm (T)Tj /T39 1 Tf 8.391 0 0 8.391 485.25 680.01 Tm (\014)Tj /F3 1 Tf 12 0 0 12 498.21 684.09 Tm 0.002 Tc 0.188 Tw [( is a)]TJ -34.01 -1.67 TD -0.001 Tc 0.271 Tw [(relative best-)-8(r)2(esponse, the )-10(resistanc)-7(e)3( of )]TJ /T40 1 Tf 8.391 0 0 8.391 306.57 659.97 Tm 0 Tc 0 Tw (K)Tj /F7 1 Tf 12.028 0 0 12.028 299.97 664.05 Tm (T)Tj /F3 1 Tf 12 0 0 12 314.61 664.05 Tm 0.001 Tc 0.279 Tw [( )10(is )10(0; )10(if the)5( c)5(h)1(a)5(nge)5( is a)5(n)1( imita)5(tion the)]TJ -18.71 -1.67 TD -0.001 Tc 0.121 Tw [(resistance )10(is )10(1; )10(if )10(the ch)-11(an)-11(g)9(e)3( is an innov)-11(ation the resistanc)-7(e)3( is )]TJ /F5 1 Tf 26.34 0 TD 0 Tc 0 Tw (M)Tj /F3 1 Tf 1.16 0 TD -0.002 Tc 0.122 Tw [(. The resi)-4(st)-4(an)-12(ce of )-10(a)]TJ -27.5 -1.66 TD 0.042 Tw [(pat)-4(h)-2( i)-4(s)-3( t)-4(h)-2(e sum)-4( of t)-4(h)-2(e resi)-4(st)-4(anc)-8(e)2( of e)-8(ach poi)-4(nt)-4( i)-4(n)-2( t)-4(h)-2(e sequen)-12(ce. Th)-12(e )-10(resi)-4(st)-4(ance)-8( )]TJ /F9 1 Tf 32.42 0 TD 0.58 Tc [(\010\014)-190(\011)]TJ /F5 1 Tf -0.47 0 TD 0 Tc 0 Tw (R)Tj /F7 1 Tf 0.85 0 TD 0.38 Tc (XX)Tj /F10 1 Tf 1.13 0.02 TD 0 Tc (%)Tj /F3 1 Tf 1.1 -0.02 TD 0.002 Tc 0.048 Tw [( is)]TJ -35.03 -1.67 TD -0.002 Tc 0.062 Tw [(t)-4(h)-2(e l)-4(east)-4( resi)-4(st)-4(anc)-8(e)2( of any)8( )-10(p)-12(a)2(t)-4(h)-2( from)-4( )]TJ /F7 1 Tf 15.33 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD 0.001 Tc 0.059 Tw [( to )]TJ /F7 1 Tf 11.931 0 0 11.931 304.77 604.05 Tm 0 Tc 0 Tw (X)Tj /F10 1 Tf 0.1308 0.0101 TD (%)Tj /F3 1 Tf 12 0 0 12 316.05 604.05 Tm -0.001 Tc 0.061 Tw (. The resistance )Tj /F9 1 Tf 7.33 0 TD 0.52 Tc (\010\011)Tj /F5 1 Tf -0.47 0 TD 0 Tc 0 Tw (R)Tj /F7 1 Tf 0.85 0 TD (U)Tj /F3 1 Tf 1.15 0 TD -0.002 Tc 0.072 Tw [( of the )]TJ /F7 1 Tf 3.23 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.003 Tc (-tree )Tj /F7 1 Tf 2.37 0 TD 0 Tc (U)Tj /F3 1 Tf 0.78 0 TD 0.002 Tc 0.068 Tw [( is)]TJ -35.01 -1.67 TD -0.001 Tc 0.191 Tw [(the sum over non-root nodes )-10(o)-11(f)2( )]TJ /F9 1 Tf 14.58 0 TD 0.58 Tc [(\010\014)-50(\010)-40(\011)580(\011)]TJ /F5 1 Tf -0.47 0 TD 0 Tc 0 Tw (R)Tj /F7 1 Tf 0.85 0 TD 0.38 Tc [(XU)-10(X)]TJ /F10 1 Tf 0.13 0.02 TD 1.371 Tc (%%)Tj /F3 1 Tf 3.35 -0.02 TD -0.002 Tc 0.202 Tw [(. The resi)-4(st)-4(ance o)-12(f)1( )]TJ /F7 1 Tf 8.6 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD (, )Tj /F9 1 Tf 1.34 0 TD 0.63 Tc (\010\011)Tj /F5 1 Tf -0.47 0 TD 0 Tc (R)Tj /F7 1 Tf 0.85 0 TD (X)Tj /F3 1 Tf 1.23 0 TD 0.001 Tc 0.199 Tw [( is the)5( le)5(a)5(s)0(t)]TJ -30.93 -1.66 TD -0.002 Tc 0.002 Tw [(resi)-4(st)-4(ance o)-12(f)1( an)-22(y)18( )]TJ /F7 1 Tf 7.19 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.001 Tc 0.001 Tw [(-tree. Th)-11(e followin)-11(g)9( Theor)-8(e)3(m is proven in Youn)-11(g)9( [)-8(1993])-8(.)]TJ /F13 1 Tf -8.13 -2.17 TD -0.002 Tc 0.002 Tw [(You)-6(n)-6(g)-2(\222s T)-5(h)-6(eorem:)]TJ /F8 1 Tf 8.02 0 TD 0 Tc 0 Tw ( )Tj /F9 1 Tf 1.04 0 TD 0.63 Tc [(\010\011)-730(\020)]TJ /F7 1 Tf -0.56 0 TD 0.34 Tc (NX)Tj /F6 1 Tf 2.22 0 TD 0 Tc (\037)Tj /F8 1 Tf 1.81 0 TD ( if and only if)Tj /F9 1 Tf 12.024 0 0 12.024 260.73 510.09 Tm 0.628 Tc [(\010\011)-768(M)629(I)630(N)-1468(\010)0(\011)]TJ /F5 1 Tf -0.4691 0 TD 6.147 Tc (RR)Tj /T41 1 Tf 8.391 0 0 8.391 314.85 506.01 Tm 0 Tc (X)Tj /F7 1 Tf 12.024 0 0 12.024 265.29 510.09 Tm 5.947 Tc (XX)Tj ET q 1 i 320.61 516.09 22.2 -14.04 re W* n BT /T42 1 Tf 8.391 0 0 8.391 320.61 506.01 Tm -0.038 Tc (\2118)Tj ET Q BT /F6 1 Tf 12.024 0 0 12.024 281.01 510.09 Tm 0 Tc (\036)Tj /T43 1 Tf 8.391 0 0 8.391 315.93 506.13 Tm (%)Tj /F10 1 Tf 12.024 0 0 12.024 345.81 510.21 Tm (%)Tj /F8 1 Tf 12 0 0 12 90.09 474.09 Tm -0.002 Tc (Remark: )Tj /F3 1 Tf 3.68 0 TD -0.001 Tc 0.001 Tw [(Th)-11(e set of )]TJ /F7 1 Tf 4.48 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.001 Tc 0.001 Tw ( for which )Tj /F9 1 Tf 5.14 0 TD 0.63 Tc [(\010\011)-730(\020)]TJ /F7 1 Tf -0.56 0 TD 0.34 Tc (NX)Tj /F6 1 Tf 2.22 0 TD 0 Tc 0 Tw (\037)Tj /F3 1 Tf 1.81 0 TD 0.001 Tc -0.001 Tw [( is c)5(a)5(lle)5(d the)5( )]TJ /F8 1 Tf 5.27 0 TD 0 Tc 0 Tw (stochastically stable set)Tj /F3 1 Tf 9.5 0 TD (.)Tj -29.48 -2.17 TD -0.002 Tc 0.092 Tw [(The basi)-4(c t)-4(ool)-4( for )-10(anal)-24(y)28(z)-8(i)-4(n)-12(g)8( )]TJ /F7 1 Tf 12.14 0 TD 0 Tc 0 Tw (N)Tj /F3 1 Tf 0.86 0 TD 0.001 Tc 0.099 Tw [( is tre)5(e)5( surg)11(e)5(r)-16(y)21(,)1( b)-19(y)21( )-10(whic)5(h we)5( t)-11(r)4(a)5(n)1(sform on)-9(e)5( tree)]TJ -16 -1.67 TD -0.001 Tc 0.051 Tw [(into another and compa)-7(r)2(e the r)-8(e)3(sistanc)-7(e)3(s of )-10(the )-10(two )-10(tre)-7(e)3(s. )-10(Suppose )-10(that )]TJ /F7 1 Tf 29.46 0 TD 0 Tc 0 Tw (U)Tj /F3 1 Tf 0.78 0 TD 0.002 Tc 0.058 Tw [( is a)6(n)2( )]TJ /F7 1 Tf 2.75 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.003 Tc (-tree.)Tj -33.93 -1.66 TD 0.062 Tw [(For an)-22(y)18( nod)-12(es )]TJ /F7 1 Tf 11.931 0 0 11.931 165.93 408.09 Tm 1.512 Tc (XX)Tj /F6 1 Tf 1.0058 0 TD 0 Tc 0 Tw (v)Tj /F10 1 Tf -0.875 0.0101 TD (%)Tj /F3 1 Tf 12 0 0 12 202.29 408.09 Tm -0.003 Tc 0.063 Tw [( we )]TJ /F8 1 Tf 1.79 0 TD (cut)Tj /F3 1 Tf 1.22 0 TD 0.001 Tc 0.069 Tw [( the)5( )]TJ /F7 1 Tf 11.931 0 0 11.931 263.49 408.09 Tm 0 Tc 0 Tw (X)Tj /F10 1 Tf 0.1308 0.0101 TD (%)Tj /F3 1 Tf 12 0 0 12 274.77 408.09 Tm 0.001 Tc 0.069 Tw [(-subtre)5(e)5( se)5(para)5(tin)-9(g)11( the)5( ori)-11(g)11(ina)5(l)-1( tree)5( into two tre)5(e)5(s)0(;)]TJ -15.39 -1.67 TD -0.001 Tc 0.271 Tw [(one the )]TJ /F7 1 Tf 11.931 0 0 11.931 137.25 388.05 Tm 0 Tc 0 Tw (X)Tj /F10 1 Tf 0.1308 0.0101 TD (%)Tj /F3 1 Tf 12 0 0 12 148.53 388.05 Tm -0.002 Tc 0.272 Tw [(-subt)-4(ree and t)-4(h)-2(e ot)-4(he)-8(r what)-4( i)-4(s)-3( l)-4(e)2(ft)-4( ov)-12(er. Thi)-4(s)-3( redu)-12(ces t)-4(h)-2(e r)-9(e)2(si)-4(st)-4(ance )-10(by)]TJ /F9 1 Tf -4.23 -1.67 TD 0.58 Tc [(\010\014)-50(\010)-40(\011)580(\011)]TJ /F5 1 Tf -0.47 0 TD 0 Tc 0 Tw (R)Tj /F7 1 Tf 0.85 0 TD 0.38 Tc [(XU)-10(X)]TJ /F10 1 Tf 0.13 0.02 TD 1.371 Tc (%%)Tj /F3 1 Tf 3.35 -0.02 TD 0 Tc 0.04 Tw [(. I)13(f)3( )]TJ /F7 1 Tf 1.7 0 TD 0 Tw (X)Tj /F10 1 Tf 0.15 0.55 TD (\))Tj /F3 1 Tf 0.79 -0.55 TD -0.001 Tc 0.031 Tw [( is a node in either of the two tr)-8(ees, and )]TJ /F9 1 Tf 16.68 0 TD 0 Tc 0 Tw (e)Tj /F7 1 Tf -0.14 0 TD (X)Tj /F3 1 Tf 0.94 0 TD -0.001 Tc 0.041 Tw [( is the root of the other tr)-8(ee,)]TJ -24.62 -1.66 TD 0.241 Tw [(we ma)-17(y)19( )]TJ /F8 1 Tf 3.86 0 TD 0.001 Tc (paste)Tj /F3 1 Tf 2.11 0 TD 0 Tc 0 Tw ( )Tj /F9 1 Tf 0.86 0 TD (e)Tj /F7 1 Tf -0.14 0 TD (X)Tj /F3 1 Tf 0.94 0 TD 0.001 Tc 0.239 Tw [( to )]TJ /F7 1 Tf 1.98 0 TD 0 Tc 0 Tw (X)Tj /F10 1 Tf 0.15 0.55 TD (\))Tj /F3 1 Tf 0.79 -0.55 TD -0.001 Tc 0.241 Tw [( b)-11(y)19( definin)-11(g)9( )]TJ /F9 1 Tf 6.52 0 TD 0.12 Tc [(\010e)110(\011)]TJ /F7 1 Tf -0.5 0 TD 0.39 Tc [(UX)-1430(X)]TJ ET q 1 i 315.21 360.09 24.12 -18 re W* n BT /F6 1 Tf 12 0 0 12 315.21 348.09 Tm 0 Tc 0 Tw (\036)Tj ET Q BT /F10 1 Tf 12 0 0 12 330.57 354.69 Tm 0 Tc 0 Tw (\))Tj /F3 1 Tf 0.73 -0.55 TD 0.001 Tc 0.249 Tw [(. )10(This tre)5(e)5( ha)5(s the)5( root o)-9(f)4( the)5( tree)]TJ -20.77 -1.67 TD 0 Tc [(containing)10( )]TJ /F7 1 Tf 4.77 0 TD 0 Tw (X)Tj /F10 1 Tf 0.15 0.55 TD (\))Tj /F3 1 Tf 0.79 -0.55 TD -0.002 Tc 0.092 Tw [(. )10(The )10(past)-4(e ope)-8(rat)-4(i)-4(on i)-4(n)-2(cr)-9(eases t)-4(h)-2(e )-10(resi)-4(st)-4(anc)-8(e)2( b)-22(y)18( )]TJ /F9 1 Tf 20.81 0 TD 0.12 Tc [(\010e)160(\014)-650(\011)]TJ /F5 1 Tf -0.47 0 TD 0 Tc 0 Tw (R)Tj /F7 1 Tf 0.85 0 TD 0.38 Tc (XX)Tj /F10 1 Tf 1.15 0.55 TD 0 Tc (\))Tj /F3 1 Tf 1.08 -0.55 TD -0.001 Tc 0.091 Tw [(, so the new tree)]TJ -29.13 -1.67 TD 0 Tc 0.04 Tw (has resistance )Tj /F9 1 Tf 6.5 0 TD 0.52 Tc [(\010\011)-1130(\010)390(e)570(\014)-250(\011)-1070(\010)-60(\014)-110(\010)-100(\011)510(\011)]TJ /F5 1 Tf -0.47 0 TD 2.54 Tc [(RR)-1040(R)]TJ /F7 1 Tf 0.85 0 TD 2.47 Tc [(UX)2090(X)90(X)2090(U)2080(X)]TJ /F6 1 Tf 1.12 0 TD 3.25 Tc (\014\016)Tj /F10 1 Tf 2.98 0.55 TD 0 Tc 0 Tw (\))Tj 2.98 -0.53 TD 1.371 Tc (%%)Tj /F3 1 Tf 3.4 -0.02 TD -0.001 Tc 0.051 Tw [(. )10(These )10(operations )10(c)-7(a)3(n be used to )-10(char)-8(acte)-7(r)2(iz)-7(e)]TJ -17.36 -1.66 TD 0.321 Tw [(cl)-3(asses )10(of )10(l)-3(e)-7(ast)-3( resi)-3(st)-3(anc)-7(e)3( t)-3(r)2(ees, b)-21(y)19( sho)-11(w)1(i)-3(n)-1(g)9( )-10(cert)-13(a)3(i)-3(n)-1( operat)-3(i)-3(on do not)-3( i)-3(n)-1(cr)-8(ease t)-3(h)-11(e)]TJ 0 -1.67 TD 0.011 Tw [(resistance. )10(Th)-11(e)-17(y)19( c)-7(a)3(n also be used )-10(as below in proof b)-21(y)19( )-10(contradi)-13(ction, showing)9( that c)-7(e)3(rtain)]TJ T* 0.061 Tw [(trees c)-7(a)3(nnot be least r)-8(e)3(sistance b)-11(ecaus)-12(e)3( it is possible to )-10(cut )-10(and )-10(paste )-10(in )-10(such )-10(a )-10(w)-9(a)-17(y)19( )-10(that)]TJ 0 -1.66 TD -0.002 Tc 0.002 Tw [(t)-4(h)-2(e resi)-4(st)-4(ance i)-4(s)-3( r)-9(e)2(duc)-8(ed.)]TJ /F8 1 Tf 0 -1.67 TD 0 Tc 0 Tw (Proof of Theorem 3.2:)Tj /F3 1 Tf 8.94 0 TD ( Suppose that )Tj /F9 1 Tf 6.42 0 TD 0.63 Tc [(\010\011)-730(\020)]TJ /F7 1 Tf -0.56 0 TD 0.34 Tc (NX)Tj /F6 1 Tf 2.22 0 TD 0 Tc (\037)Tj /F3 1 Tf 1.81 0 TD ( and that )Tj /F7 1 Tf 3.93 0 TD (X)Tj /F3 1 Tf 0.94 0 TD -0.001 Tc 0.011 Tw [( is not a sing)9(leton pure pro)-11(f)2(ile.)]TJ -23.7 -1.67 TD -0.011 Tc [(Le)-7(t)-13( )]TJ /F7 1 Tf 1.8 0 TD 0 Tc 0 Tw (U)Tj /F3 1 Tf 0.78 0 TD -0.001 Tc 0.001 Tw [( be a l)-3(e)-7(ast)-3( resi)-3(st)-3(anc)-7(e)3( )]TJ /F7 1 Tf 8.65 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD -0.001 Tc 0.021 Tw [(-tree. L)10(e)3(t )]TJ /F5 1 Tf 11.931 0 0 11.931 310.65 188.01 Tm 0 Tc 0 Tw (S)Tj /F7 1 Tf -2.0719 0 TD (X)Tj /F6 1 Tf 1.0058 0 TD (\036)Tj /F10 1 Tf -0.875 0.0101 TD (%)Tj /F3 1 Tf 12 0 0 12 319.29 188.01 Tm -0.001 Tc 0.011 Tw [( be a sin)-11(g)9(leton pure str)-8(a)3(te)-7(g)-11(y)19( that is pla)-17(y)19(ed)]TJ -19.1 -1.66 TD 0.001 Tc 0.039 Tw [(with positive)5( proba)5(bilit)-11(y)31( b)-19(y)21( some)5( )]TJ /F7 1 Tf 11.931 0 0 11.931 259.17 168.09 Tm 1.37 Tc (TX)Tj /F6 1 Tf 0.9454 0 TD 0 Tc 0 Tw (\211)Tj /F3 1 Tf 12 0 0 12 292.77 168.09 Tm 0.001 Tc 0.049 Tw [(, tha)5(t)-1( is, )]TJ /F9 1 Tf 6.08 0 TD 0.63 Tc (\010\011)Tj ET q 1 i 337.53 180.09 44.88 -18 re W* n BT /F5 1 Tf 12 0 0 12 337.53 168.09 Tm 1.319 Tc (S3)Tj ET Q BT /F7 1 Tf 12 0 0 12 370.29 168.09 Tm 0 Tc 0 Tw (X)Tj /F6 1 Tf -1.94 0 TD (\211)Tj /F3 1 Tf 3.13 0 TD 0.001 Tc 0.049 Tw [(. Cutting)11( )]TJ /F7 1 Tf 11.931 0 0 11.931 433.41 168.09 Tm 0 Tc 0 Tw (X)Tj /F10 1 Tf 0.1307 0.0101 TD (%)Tj /F3 1 Tf 12 0 0 12 444.69 168.09 Tm 0.05 Tw [( and pasting)10( th)-10(e)]TJ -29.55 -1.67 TD (root )Tj /F7 1 Tf 2.12 0 TD 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD 0.002 Tc 0.038 Tw [(to it. Sinc)6(e)6( )]TJ /F7 1 Tf 11.931 0 0 11.931 185.61 148.05 Tm 0 Tc 0 Tw (X)Tj /F10 1 Tf 0.1308 0.0101 TD (%)Tj /F3 1 Tf 12 0 0 12 196.89 148.05 Tm 0.04 Tw [( is a sing)10(leton pure pro)-10(f)3(ile, it requires )-10(at least )-10(one )-10(innovation )-10(to )-20(g)10(o)]TJ -8.9 -1.67 TD 0.002 Tc 0.198 Tw [(a)6(n)-8(y)22(w)-6(he)6(re)6(, so c)6(u)2(tting)12( )-10(re)6(duce)6(s)1( the)6( re)6(sista)6(n)2(c)6(e)6( b)-18(y)22( )-10(a)6(t)0( le)6(a)6(s)1(t )]TJ /F5 1 Tf 23.81 0 TD 0 Tc 0 Tw (N)Tj /F3 1 Tf 0.91 0 TD -0.001 Tc 0.211 Tw [(. On the other hand, since)]TJ /F7 1 Tf 11.931 0 0 11.931 92.49 108.09 Tm 1.37 Tc (TX)Tj /F6 1 Tf 0.9454 0 TD 0 Tc 0 Tw (\211)Tj /F3 1 Tf 12 0 0 12 126.09 108.09 Tm -0.001 Tc 0.011 Tw [( and )]TJ /F9 1 Tf 2.73 0 TD 0.62 Tc [(\010\011)-740(\020)]TJ /F7 1 Tf -0.57 0 TD 0.369 Tc (TX)Tj /F6 1 Tf 2.22 0 TD 0 Tc 0 Tw (\037)Tj /F10 1 Tf -1.15 0.02 TD (%)Tj /F3 1 Tf 2.98 -0.02 TD -0.001 Tc 0.011 Tw [(, we c)-7(a)3(n )-10(g)9(o)-1( from )]TJ /F7 1 Tf 7.27 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD 0.001 Tc 0.009 Tw [( to )]TJ ET q 1 i 317.37 119.01 11.28 -13.92 re W* n BT /F7 1 Tf 11.931 0 0 11.931 317.37 108.09 Tm 0 Tc 0 Tw (X)Tj ET Q q 1 i 318.93 119.01 9.72 -13.92 re W* n BT /F10 1 Tf 11.931 0 0 11.931 318.93 108.21 Tm 0 Tc 0 Tw (%)Tj ET Q BT 12 0 0 12 328.65 108.09 Tm 0.009 Tc 0.001 Tw [( by)29( n)9(o)9( )-10(m)7(o)9(re)13( )-10(t)7(h)9(a)13(n)9( )]TJ /F5 1 Tf 7.28 0 TD 0 Tc 0 Tw (M)Tj /F3 1 Tf 1.16 0 TD 0.001 Tc 0.019 Tw [( imita)5(tions, pa)5(sting)]TJ -28.32 -1.67 TD 0 Tc 0.15 Tw [(the)4( root to )]TJ /F7 1 Tf 11.931 0 0 11.931 150.45 88.05 Tm 0 Tw (X)Tj /F10 1 Tf 0.1308 0.0101 TD (%)Tj /F3 1 Tf 12 0 0 12 161.73 88.05 Tm -0.002 Tc 0.162 Tw [( i)-4(n)-2(creas)-13(es t)-4(h)-2(e resi)-4(st)-4(an)-12(ce b)-22(y)18( at)-4( m)-4(o)-2(st)-4( )]TJ /F5 1 Tf 15.54 0 TD 0 Tc 0 Tw (M)Tj /F3 1 Tf 1.16 0 TD 0.16 Tw [(. B)-13(y)20( the assumption of unlikely)]TJ ET endstream endobj 98 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F3 38 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F10 61 0 R /F13 99 0 R /T33 100 0 R /T34 101 0 R /T35 102 0 R /T36 103 0 R /T37 104 0 R /T38 105 0 R /T39 106 0 R /T40 107 0 R /T41 108 0 R /T42 109 0 R /T43 110 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 111 0 obj << /Length 9716 >> stream BT /F3 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc 0 Tw (8)Tj -17.75 -3 TD 0.32 Tw [(innovation, this impl)8(i)-2(es that the new tree h)-10(a)4(s strictly)20( )-10(l)-12(e)4(ss resistanc)-6(e)4( than )-10(the )-10(old)]TJ /F4 1 Tf 0 -1.66 TD -0.001 Tc 0.001 Tw [(contradictin)-11(g)9( Youn)-11(g)9(\222)2(s Th)-11(eorem.)]TJ /F12 1 Tf 35.11 -1.67 TD 0 Tc 0 Tw (\346)Tj /F1 1 Tf 14.04 0 0 14.04 90.09 632.01 Tm 0.004 Tw [(4. W)21(i)-4(nning Pa)9(ir)13(w)-17(i)4(se )8(Contest)25(s)9( is)9( Suff)8(icient)]TJ /F4 1 Tf 12 0 0 12 126.09 609.09 Tm 0.001 Tc 0.089 Tw [(We)5( now e)5(s)0(ta)5(blish our first ma)5(in re)5(sult: we)5( show tha)5(t)-1( if )-10(a)5( pure)5( stra)5(teg)-9(y)21( )-10(bea)5(t)-1(s )-10(a)5(l)-1(l)]TJ -3 -1.67 TD 0 Tc 0.08 Tw [(others )10(in )10(pairwise )10(cont)-12(ests, )10(then )10(it is the unique stochasticall)-12(y)20( stabl)-12(e)4( state. W)-6(e)4( be)-6(g)10(i)-2(n b)-20(y)]TJ T* 0 Tw [(ex)-10(plaining)10( what it means to win pairwise )-10(contests.)]TJ /F11 1 Tf 0 -2.16 TD 0.33 Tw [(Def)-7(i)-2(nition 4.1:)]TJ /F8 1 Tf 6.45 0 TD 0.34 Tw [( Suppose that )]TJ /F9 1 Tf 7.21 0 TD 0 Tw (\014)Tj /F5 1 Tf -0.4 0 TD 0.339 Tc [(SS)-1040(3)]TJ /F6 1 Tf 1.6 0 TD 0 Tc (\211)Tj /F10 1 Tf -0.78 0.03 TD (%)Tj /F8 1 Tf 2.69 -0.03 TD 0.34 Tw (. For )Tj ET q 1 i 329.13 555.09 54.36 -17.04 re W* n BT /F9 1 Tf 12.028 0 0 12.028 329.13 543.09 Tm 3.288 Tc (\020\021)Tj ET Q BT /F5 1 Tf 12.028 0 0 12.028 351.57 543.09 Tm 0 Tw (X)Tj ET q 1 i 338.85 555.09 44.64 -17.04 re W* n BT /F6 1 Tf 12.028 0 0 12.028 338.85 543.09 Tm 1.167 Tc (bb)Tj ET Q BT /F8 1 Tf 12 0 0 12 383.49 543.09 Tm 0.001 Tc 0.339 Tw [( de)5(fine)5( a family)5( of mix)5(e)5(d)]TJ -24.45 -1.67 TD 0 Tc (strategies )Tj /F9 1 Tf 4.91 0 TD 0.5 Tc (\010\011)Tj /F5 1 Tf 0.34 0 TD 0 Tc 0 Tw (X)Tj /F7 1 Tf -0.91 0 TD (T)Tj /F8 1 Tf 2.05 0 TD -0.001 Tc 0.001 Tw ( by )Tj /F9 1 Tf 2.21 0 TD 0.5 Tc [(\010\011)500(;)50(=)-1350(\014)-170(\010)0(\011)500(;)-10(=)-810(\021)]TJ /F5 1 Tf 0.34 0 TD 0.701 Tc [(XS)-1018(X)-620(X)-10(S)-2668(X)]TJ /F7 1 Tf -0.91 0 TD 4.529 Tc (TT)Tj /F6 1 Tf 3.11 0 TD 4.376 Tc [(\036\036)3410(\016)]TJ /F10 1 Tf 4.14 0.03 TD 0 Tc 0 Tw (%)Tj /F8 1 Tf 4.55 -0.03 TD (. If for all)Tj /F9 1 Tf 6.2 0 TD 0.06 Tc [(\021\017)-50(\022)]TJ /F5 1 Tf -1.92 0 TD 0 Tc (X)Tj /F6 1 Tf 0.89 0 TD (p)Tj /F9 1 Tf -11.91 -2.34 TD [(\010)-330(\014)-670(\010)-500(\011)0(\011)-1670(\010)-390(\014)-670(\010)-500(\011\011)-1360(\020)]TJ /F5 1 Tf -0.55 0 TD 0.32 Tc [(US)-969(X)-1671(U)0(S)-1029(X)]TJ /F7 1 Tf 1.66 0 TD 4.499 Tc (TT)Tj /F6 1 Tf 2.4 0 TD 4.37 Tc (\016\037)Tj /F10 1 Tf 1.89 0.03 TD 0 Tc (%)Tj /F8 1 Tf -18.49 -2.86 TD (we say that )Tj /F5 1 Tf 4.91 0 TD (S)Tj /F8 1 Tf 0.76 0 TD ( )Tj /F11 1 Tf 0.25 0 TD -0.001 Tc (beats)Tj /F8 1 Tf 2.22 0 TD 0 Tc ( )Tj /F5 1 Tf 11.931 0 0 11.931 192.69 461.01 Tm (S)Tj /F10 1 Tf 0.0704 0.0302 TD (%)Tj /F8 1 Tf 12 0 0 12 201.81 461.01 Tm (.)Tj /F11 1 Tf -9.31 -2.66 TD -0.001 Tc 0.181 Tw [(Theore)-7(m)12( 4.1:)]TJ /F8 1 Tf 5.89 0 TD 0 Tc 0.18 Tw [( Suppose unlikely innovation, sufficiently large )]TJ /F5 1 Tf 20.3 0 TD 0 Tw (N)Tj /F8 1 Tf 0.91 0 TD 0.001 Tc 0.189 Tw [( and that )]TJ /F5 1 Tf 4.53 0 TD 0 Tc 0 Tw (S)Tj /F8 1 Tf 0.76 0 TD 0.19 Tw (beats all)Tj /F5 1 Tf 11.931 0 0 11.931 92.01 409.05 Tm 1.52 Tc (SS)Tj /F6 1 Tf 0.865 0 TD 0 Tc 0 Tw (v)Tj /F10 1 Tf -0.7946 0.0302 TD (%)Tj /F8 1 Tf 12 0 0 12 124.05 409.05 Tm (. Then )Tj /F9 1 Tf 3.53 0 TD [(\010[)-350(]\011)-1340(\021)]TJ /F5 1 Tf 0.8 0 TD (S)Tj /F7 1 Tf -1.36 0 TD (N)Tj /F6 1 Tf 2.97 0 TD (\036)Tj /F8 1 Tf 1.73 0 TD (.)Tj -10.5 -2.17 TD -0.001 Tc (Proof: )Tj /F4 1 Tf 2.94 0 TD 0.081 Tw [(Suppose that there is other )-10(some )]TJ /F7 1 Tf 13.94 0 TD 0 Tc 0 Tw (X)Tj /F4 1 Tf 0.94 0 TD 0.001 Tc 0.089 Tw [( with )]TJ ET q 1 i 342.81 395.01 41.64 -18 re W* n BT /F9 1 Tf 12 0 0 12 342.81 383.01 Tm 0.63 Tc [(\010\011)-730(\020)]TJ ET Q q 1 i 336.09 395.01 35.28 -18 re W* n BT /F7 1 Tf 12 0 0 12 336.09 383.01 Tm 0.34 Tc (NX)Tj ET Q BT /F6 1 Tf 12 0 0 12 362.73 383.01 Tm 0 Tc 0 Tw (\037)Tj /F4 1 Tf 1.81 0 TD 0.09 Tw [(. B)-13(y)20( Theor)-7(e)4(m 3.2 )]TJ /F9 1 Tf 10.42 0.02 TD 0 Tw (e)Tj -0.48 -0.02 TD 0.35 Tc ([])Tj /F5 1 Tf 0.4 0 TD 0 Tc (S)Tj /F7 1 Tf -2.48 0 TD (X)Tj /F6 1 Tf 1 0 TD (\036)Tj /F4 1 Tf -33.39 -1.66 TD -0.001 Tc 0.061 Tw [(for some pure str)-8(a)3(te)-7(g)-11(y)19( )]TJ /F9 1 Tf 9.7 0.02 TD 0 Tc 0 Tw (e)Tj /F5 1 Tf -0.08 -0.02 TD (S)Tj /F4 1 Tf 0.76 0 TD 0.001 Tc 0.059 Tw [(. L)12(e)5(t )]TJ /F7 1 Tf 2.42 0 TD 0 Tc 0 Tw (U)Tj /F4 1 Tf 0.78 0 TD -0.002 Tc 0.062 Tw [( be t)-4(h)-2(e l)-4(east)-4( r)-9(e)2(si)-4(st)-4(ance )]TJ /F7 1 Tf 9.71 0 TD 0 Tc 0 Tw (X)Tj /F4 1 Tf 0.94 0 TD 0.06 Tw [(-tre)-6(e. Since it is not )-10(the )-10(root,)]TJ -24.23 -1.67 TD -0.001 Tc 0.041 Tw [(we )10(ma)-17(y)19( suppose that )]TJ /F9 1 Tf 8.93 0 TD 0.35 Tc ([])Tj /F5 1 Tf 0.41 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 1.17 0 TD 0.001 Tc 0.039 Tw [( is a)5(tta)5(c)5(h)1(e)5(d)1( to some)5( )]TJ ET q 1 i 318.93 353.97 11.28 -13.92 re W* n BT /F7 1 Tf 11.931 0 0 11.931 318.93 343.05 Tm 0 Tc 0 Tw (X)Tj ET Q q 1 i 320.49 353.97 9.72 -13.92 re W* n BT /F10 1 Tf 11.931 0 0 11.931 320.49 343.17 Tm 0 Tc 0 Tw (%)Tj ET Q BT 12 0 0 12 330.21 343.05 Tm [(, a)5(nd c)5(onside)5(r)4( c)5(u)1(ttin)-9(g)11( it a)5(nd pa)5(sting the)]TJ -20.01 -1.67 TD 0 Tc 0.07 Tw [(root )10(to )10(it. )-10(I)23(t)-2( took at least one innovation plus, since )]TJ /F5 1 Tf 21.49 0 TD 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD 0.07 Tw [( beats an)-20(y)20( point in )]TJ /F7 1 Tf 11.931 0 0 11.931 454.89 323.01 Tm 0 Tw (X)Tj /F10 1 Tf 0.1308 0.0101 TD (%)Tj /F4 1 Tf 12 0 0 12 466.17 323.01 Tm 0.07 Tw [(, more)4( tha)4(n)]TJ /F9 1 Tf -30.17 -1.66 TD 0.11 Tc (\017\022)Tj /F5 1 Tf -1 0 TD 0 Tc 0 Tw (M)Tj /F4 1 Tf 2.33 0 TD 0.001 Tc 0.309 Tw [( imita)5(tions to g)11(e)5(t to )]TJ /F7 1 Tf 11.931 0 0 11.931 237.69 303.09 Tm 0 Tc 0 Tw (X)Tj /F10 1 Tf 0.1308 0.0101 TD (%)Tj /F4 1 Tf 12 0 0 12 248.97 303.09 Tm -0.002 Tc 0.312 Tw [(, so t)-4(h)-2(e resi)-4(st)-4(ance i)-4(s)-3( r)-9(e)2(duced )-10(by)8( )-20(st)-4(ri)-14(ct)-4(l)-14(y)18( )-10(m)-4(o)-2(r)-9(e)2( )-10(t)-4(h)-2(an)]TJ /F9 1 Tf -10.19 -1.67 TD 0.11 Tc (\017\022)Tj /F5 1 Tf -2.88 0 TD 1.317 Tc (NM)Tj /F6 1 Tf 0.89 0 TD 0 Tc 0 Tw (\014)Tj /F4 1 Tf 3.36 0 TD -0.001 Tc 0.191 Tw [(. Howeve)-7(r, since )]TJ /F5 1 Tf 7.7 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD -0.002 Tc 0.192 Tw [( beat)-4(s )]TJ /F9 1 Tf 3.18 0.02 TD 0 Tc 0 Tw (e)Tj /F5 1 Tf -0.08 -0.02 TD (S)Tj /F4 1 Tf 0.76 0 TD -0.002 Tc 0.192 Tw [( we can g)8(e)2(t)-4( f)-9(r)1(om)-4( )]TJ /F9 1 Tf 10.68 0.02 TD 0 Tc 0 Tw (e)Tj -0.48 -0.02 TD 0.35 Tc ([])Tj /F5 1 Tf 0.4 0 TD 0 Tc (S)Tj /F7 1 Tf -2.48 0 TD (X)Tj /F6 1 Tf 1 0 TD (\036)Tj /F4 1 Tf 2.61 0 TD 0.001 Tc 0.189 Tw [( to )]TJ /F9 1 Tf 1.83 0 TD 0.35 Tc ([])Tj /F5 1 Tf 0.41 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 1.17 0 TD 0.2 Tw [( with one)]TJ -31.88 -1.67 TD 0.34 Tw [(innovation and no more than )]TJ /F9 1 Tf 14.62 0 TD 0.11 Tc (\017\022)Tj /F5 1 Tf -1 0 TD 0 Tc 0 Tw (M)Tj /F4 1 Tf 2.33 0 TD 0.001 Tc 0.349 Tw [( imita)5(tions. So re)5(sista)5(n)1(c)5(e)5( is stric)5(t)-1(l)-11(y)31( )-10(re)5(duce)5(d)]TJ -15.95 -1.66 TD -0.001 Tc 0.001 Tw [(contradictin)-11(g)9( Youn)-11(g)9(\222)2(s Th)-11(eorem.)]TJ /F12 1 Tf 35.11 -1.67 TD 0 Tc 0 Tw (\346)Tj /F4 1 Tf -32.11 -1.67 TD 0.01 Tw [(The )10(h)-10(y)20(poth)-10(e)4(sis, that when half o)-10(r)3( more of th)-10(e population is pla)-6(y)20(in)-10(g)10( )]TJ /F5 1 Tf 27.46 0 TD 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD -0.003 Tc 0.013 Tw [( a)-9(g)7(ai)-5(nst)-5( an)-13(y)]TJ -31.22 -1.66 TD -0.001 Tc 0.071 Tw [(other pure pro)-11(f)2(ile, all play)9(e)-7(r)-8(s pre)-7(f)2(er to )-10(pla)-17(y)19( )]TJ /F5 1 Tf 18.26 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD -0.002 Tc 0.082 Tw [( i)-4(s)-3( connect)-4(ed t)-4(o)-2( t)-4(h)-2(e i)-4(d)-2(e)-8(a)2( of \275-dom)-4(i)-4(n)-2(ance)]TJ -19.02 -1.67 TD -0.001 Tc 0.101 Tw [(introduced b)-21(y)19( Morris, Rob and Shin [)-8(1993])-8(. The concept )-10(of )-10(\275-dominan)-11(ce )-10(is )-10(that )-10(when)]TJ T* 0 Tc 0.01 Tw [(half or more o)-10(f)3( the population is pla)-6(y)20(in)-10(g)10( )]TJ /F5 1 Tf 16.68 0 TD 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD -0.001 Tc 0.011 Tw [( a)-7(g)9(ainst an)-21(y)19( other )-10(combination of strateg)9(i)-3(es, )-10(it)]TJ -17.44 -1.66 TD 0.081 Tw [(is a best response to pla)-17(y)19( )]TJ /F5 1 Tf 10.86 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD -0.002 Tc 0.082 Tw [(. The conc)-8(ept)-4( her)-9(e)2( i)-4(s)-3( weak)-12(er )-10(i)-4(n)-2( )-10(t)-4(w)0(o )-10(r)-9(e)2(spect)-4(s:)-4( )-10(fi)-4(rst)-4(,)-2( )]TJ /F5 1 Tf 21.34 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD 0.001 Tc 0.089 Tw [( mus)10(t)]TJ -33.72 -1.67 TD 0 Tc 0.16 Tw [(onl)-12(y)20( be)-6(at pure pro)-10(f)3(iles, not arbitra)-6(r)-17(y)20( combinations of strate)-6(g)10(i)-12(es. Second, )]TJ /F5 1 Tf 30.96 0 TD 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD 0.001 Tc 0.169 Tw [( mus)10(t)-1( win)]TJ -31.72 -1.67 TD -0.001 Tc 0.011 Tw [(onl)-13(y)19( )10(in )10(the sense o)-11(f)2( being a )-10(relative best)-13(-response, it ne)-7(ed not actu)-11(a)3(ll)-13(y)19( b)-11(e)3( a best-res)-12(ponse;)]TJ ET endstream endobj 112 0 obj << /ProcSet [/PDF /Text ] /Font << /F1 36 0 R /F3 38 0 R /F4 43 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F10 61 0 R /F11 62 0 R /F12 90 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 113 0 obj << /Length 6362 >> stream BT /F3 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc 0 Tw (9)Tj -17.75 -3 TD 0.001 Tc 0.099 Tw [(a)5( third stra)5(teg)-9(y)21( ma)-15(y)21( ac)5(tua)5(l)-1(l)-21(y)21( do )-10(be)5(tte)5(r )-10(tha)5(n)1( )]TJ /F5 1 Tf 18.37 0 TD 0 Tc 0 Tw (S)Tj /F3 1 Tf 0.76 0 TD 0.001 Tc 0.109 Tw [(, a)5(nd this is sig)11(n)1(ific)5(a)5(n)1(t )-10(a)5(s)0( we)5( will se)5(e)5( in)]TJ /F4 1 Tf -19.13 -1.66 TD -0.001 Tc 0.121 Tw [(ex)-11(amples )10(below. )10(On )10(the other hand, \275)-11(-)2(dominance c)-7(l)-3(ea)-7(rl)-13(y)19( implies winnin)-11(g)9( all pairwis)-12(e)]TJ 0 -1.67 TD 0 Tc 0.14 Tw [(contests, so if there is a \275-dominant str)-7(a)4(te)-6(g)-10(y)20(, from Mor)-7(r)3(is, Rob and Shin )-10([)-7(1993])-7( )-10(it)8( )-10(is)]TJ T* 0.001 Tc 0.289 Tw [(stoc)5(ha)5(stic)5(a)5(l)-1(l)-11(y)21( sta)5(b)1(l)-11(e)5( with re)5(spec)5(t to the)5( usua)5(l e)5(volutiona)5(r)-16(y)21( d)-19(y)21(n)-9(a)5(mic)5(, a)5(nd it is a)5(l)-1(so)]TJ 0 -1.66 TD 0 Tc 0.03 Tw [(stochasticall)-12(y)20( stabl)-12(e)4( when innovation is unlikel)-12(y)20(.)0( Ex)-10(amples below will show )-10(cl)-12(early)10( )-20(how)]TJ 0 -1.67 TD -0.001 Tc 0.071 Tw [(the usual notion of stochastic stabilit)-13(y)19( and the )-10(case o)-11(f)2( unlikel)-23(y)19( innovation )-10(diver)-8(g)9(e )-10(wh)-11(en)]TJ T* 0.001 Tc 0.109 Tw [(\275-domina)5(n)1(c)5(e)5( fa)5(ils, a)5(s)0( we)5(ll illustra)5(ting)11( tha)5(t)-1( in inte)5(re)5(stin)-9(g)11( )-10(g)11(a)5(m)-11(e)5(s the)5(r)4(e)5( )-10(c)5(a)5(n)1( b)-9(e)5( a)5( )-10(stra)5(teg)-9(y)]TJ 0 -1.66 TD 0 Tc 0 Tw [(that wins all pairwise contests, ev)-10(en thoug)10(h th)-10(ere is no \275-dominant str)-7(a)4(te)-6(g)-10(y)20(.)]TJ 3 -1.67 TD 0.1 Tw [(I)13(n)0(te)-6(restin)-10(g)10(l)-12(y)20(,)0( )-10(Kandori )-10(and Rob [)-7(1993])-7( stud)-10(y)30( a cl)-12(ass of )-10(g)10(a)4(mes in which )-20(winning)]TJ -3 -1.67 TD 0.01 Tw [(all )10(pairwise )10(contests )10(implies \275-dominance. )-10(The)-16(y)20( stud)-20(y)20( sing)10(l)-12(e)4( population matching)10( )-10(games)]TJ 0 -1.66 TD -0.001 Tc 0.101 Tw [(satisf)-8(y)19(in)-11(g)9( the \223total b)-11(a)3(ndwa)-7(g)9(on p)-11(r)2(opert)-23(y)19(\224)3( m)-13(eanin)-11(g)9( that the best r)-8(e)3(sponse )-10(to )-10(an)-21(y)19( )-10(mix)-11(ed)]TJ 0 -1.67 TD 0 Tc 0.08 Tw [(strate)-6(g)-10(y)20( is contained in the support of th)-10(at mix)-10(ed strateg)-10(y)20(. )-10(I)13(n)0( p)-10(a)4(rticular, this means )-10(that)]TJ T* 0.03 Tw [(a)4(n)-10(y)20( )10(pu)-10(re)4( )10(pro)-10(f)3(ile)4( is a)4( Na)4(sh )-10(e)4(quilibrium. They)20( m)-12(a)4(ke)4( se)4(v)-10(e)4(ra)4(l other a)4(ssumptions a)4(s)-1( we)4(ll, but)]TJ 0 -1.66 TD -0.001 Tc 0.111 Tw [(as )10(F)5(udenb)-11(er)-8(g)9( )10(and )-10(L)10(e)3(vine )10([)-8(1998])-8( )10(point out, these other assumptions are redund)-11(ant. )-10(I)12(n)-1( a)]TJ 0 -1.67 TD 0.081 Tw [(g)9(a)3(m)-13(e)3( )10(satisf)-18(y)29(in)-11(g)9( th)-11(e \223total bandw)-9(a)-7(g)9(on prop)-11(ert)-23(y)19(\224 if )]TJ /F5 1 Tf 21.01 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD 0.001 Tc 0.079 Tw [( wins a)5(ll pa)5(irwise)5( c)5(onte)5(s)0(ts, it must)]TJ -21.77 -1.67 TD -0.001 Tc 0.031 Tw [(be actuall)-23(y)19( be )-10(a best-r)-8(esponse a)-7(g)-1(ainst ever)-18(y)19( oth)-11(e)3(r pur)-8(e strate)-7(g)-11(y)19( wh)-11(en \275 the population )-10(is)]TJ 0 -1.66 TD 0.002 Tc [(pla)-4(y)22(in)-8(g)12( )]TJ /F5 1 Tf 3.5 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD 0.1 Tw [(. Since utilit)-12(y)30( is linear in the popul)-12(ation distribution of strateg)10(i)-2(es, this means)]TJ -4.26 -1.67 TD 0.001 Tc [(tha)5(t)-1( )]TJ /F5 1 Tf 2.17 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD -0.001 Tc 0.261 Tw [( is actuall)-13(y)19( b)-11(e)3(st response )-10(a)-7(g)9(ainst an)-21(y)19( combination of strat)-13(e)-7(g)9(i)-3(es when \275 the)]TJ -2.93 -1.67 TD 0.001 Tc -0.001 Tw [(population is pla)-5(y)31(in)-9(g)11( )]TJ /F5 1 Tf 8.85 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD -0.001 Tc 0.001 Tw (, so in fact )Tj /F5 1 Tf 4.58 0 TD 0 Tc 0 Tw (S)Tj /F4 1 Tf 0.76 0 TD [( is in fa)4(c)4(t)-2( \275-domina)4(n)0(t.)]TJ /F2 1 Tf -14.95 -2.66 TD 0.004 Tc -0.002 Tw [(Ex)14(ampl)6(e )10(4.1:)12( A S)11(peci)6(a)0(l)6(i)6(z)14(ati)6(on G)12(a)0(m)7(e)]TJ /F4 1 Tf 3 -1.92 TD 0.001 Tc 0.219 Tw [(We)5( now stud)-9(y)21( a)5( simple)5( )-10(g)11(a)5(me)5( )-10(with a)5( unique)5( e)5(quilibrium tha)5(t)-1( is )-10(mix)-9(e)5(d. )-10(This)]TJ -3 -1.67 TD 0 Tc 0.01 Tw [(illustrates )10(that )10(unlikel)-12(y)20( )10(innovation )10(can )10(b)-10(e)4( quite different than unlikel)-22(y)20( imitation. Consider)]TJ 0 -1.66 TD 0.002 Tc 0.008 Tw [(a)6( simple)6( )]TJ /F9 1 Tf 3.82 0 TD 1.04 Tc (\022\022)Tj /F6 1 Tf 0.64 0 TD 0 Tc 0 Tw (q)Tj /F4 1 Tf 1.67 0 TD 0.02 Tw [(s)-11(y)20(mmetric game )10(of )10(spe)-6(c)4(ializ)-6(ation: )10(pla)-6(y)20(e)-6(r)3(s ma)-16(y)20( speci)-12(aliz)-6(e in being)10( hunters)]TJ -6.13 -1.67 TD -0.001 Tc 0.211 Tw [(or )10(gather)-8(ers. I)12(f)2( )10(both choose )10(the )10(sam)-13(e)3( specializ)-7(ation the)-17(y)19( consume onl)-23(y)19( one p)-11(r)2(oduct,)]TJ T* 0 Tc 0.04 Tw [(resulting)10( in a utilit)-12(y)20( of zero. )-20(I)13(f)3( the)-16(y)20( )-10(choose diff)-7(erent sp)-10(ecializations they)20( tr)-7(ade, )-10(consum)-12(e)]TJ 0 -1.66 TD 0 Tw [(both products, and )-10(g)10(e)4(t a utilit)-12(y)20( of on)-10(e. The p)-10(a)-16(y)20(o)0(ff mat)-12(r)3(ix)-10( is)]TJ /F11 1 Tf 4.46 -3.35 TD 0.004 Tc [(Hunt)-1333(G)12(a)4(t)7(h)0(e)8(r)]TJ ET 1 i 137.85 164.97 0.6 -19.92 re f 180.69 164.97 0.6 -19.92 re f BT 12 0 0 12 90.09 128.25 Tm (Hunt)Tj /F4 1 Tf 4.46 0 TD 0 Tc [(0,0)-2320(1,1)]TJ ET 84.69 144.93 53.04 -0.6 re f 137.85 144.93 0.6 -0.6 re f 138.57 144.93 42 -0.6 re f 180.69 144.93 0.6 -0.6 re f 181.41 144.93 53.04 -0.6 re f 137.85 144.21 0.6 -19.92 re f 180.69 144.21 0.6 -19.92 re f BT /F11 1 Tf 12 0 0 12 90.09 107.49 Tm -0.005 Tc [(Ga)-5(th)-9(er)]TJ /F4 1 Tf 4.46 0 TD 0 Tc [(1,1)-2320(0,0)]TJ ET 84.69 124.17 53.04 -0.6 re f 137.85 124.17 0.6 -0.6 re f 138.57 124.17 42 -0.6 re f 180.69 124.17 0.6 -0.6 re f 181.41 124.17 53.04 -0.6 re f 137.85 123.45 0.6 -19.92 re f 180.69 123.45 0.6 -19.92 re f endstream endobj 114 0 obj << /ProcSet [/PDF /Text ] /Font << /F2 37 0 R /F3 38 0 R /F4 43 0 R /F5 46 0 R /F6 47 0 R /F9 50 0 R /F11 62 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 116 0 obj << /Length 6503 >> stream BT /F3 1 Tf 12 0 0 12 300.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc (10)Tj -17.5 -3 TD 0.001 Tc 0.009 Tw [(We)5( first a)5(ssume)5( tha)5(t)-1( this is play)21(e)5(d)1( a)5(s)0( )-10(a)5(n)1( a)5(non)-19(y)21(m)-1(ous ma)5(tc)5(hin)-9(g)11( )-10(g)11(a)5(m)-11(e)5(. This )-10(me)5(a)5(n)1(s )-10(the)5( )-10(onl)-21(y)]TJ 0 -1.66 TD -0.001 Tc 0.071 Tw [(pure strate)-7(g)9(i)-3(es )-10(are )-10(Hunt and Gath)-11(er. )-10(F)5(r)2(om s)-22(y)29(mm)-13(etr)-18(y)19( it is obvious both must have equal)]TJ /F4 1 Tf 0 -1.67 TD 0 Tc 0 Tw [(weig)10(ht \(o)-10(f \275\) in the limit distribution with )-10(unlikely)20( )-10(innovation. )-10(This )-10(is )-10(ver)-17(y)20( )-10(diff)-7(erent )-10(than)]TJ T* 0.001 Tc 0.019 Tw [(the)5( c)5(a)5(s)0(e)5( the)5( st)-11(a)5(nda)5(rd )-10(c)5(a)5(s)0(e)5(:)-1( the)5( mix)-9(e)5(d)1( e)5(quilibrium is the)5( unique)5( Na)5(sh e)5(quilibrium a)5(nd it )-10(is)]TJ 0 -1.66 TD 0 Tc 0.1 Tw [(the unique point in )]TJ /F6 1 Tf 8.37 0 TD 0 Tw (8)Tj /F4 1 Tf 0.97 0 TD -0.001 Tc 0.111 Tw [( )10(since )10(pla)-7(y)19(e)-7(r)2(s )10(pr)-8(efe)-7(r)2( to do the opposite of wh)-11(at ever)-18(y)19(o)-1(n)-11(e)3( else is)]TJ -9.34 -1.67 TD 0 Tc 0.33 Tw [(doing)10(. )10(This )10(means )10(that )10(it )10(takes )10(on)-10(e innovation to g)10(e)4(t to the b)-10(a)4(sin of the mix)-10(ed)]TJ T* 0.06 Tw [(equilibrium, )10(while )10(it takes half the population to innovate to get out of the basin. Notice)]TJ 0 -1.66 TD 0.27 Tw [(that )10(even with unlikel)-12(y)20( imitation, we continue to )-10(assume the rel)-12(a)4(tive best-response)]TJ 0 -1.67 TD 0.04 Tw [(d)-10(y)20(namic, but this makes little difference as it takes onl)-22(y)20( )-10(a )-10(sin)-10(g)10(le )-10(innovation )-10(to )-20(g)10(e)4(t )-10(out )-10(of)]TJ T* 0 Tw (the non-Nash points in )Tj /F6 1 Tf 9.52 0 TD (8)Tj /F4 1 Tf 0.97 0 TD (.)Tj -7.49 -1.66 TD 0.01 Tw [(We )10(should )10(dig)10(r)3(ess )10(briefly)20( to )10(discuss how mix)-10(ed strateg)-10(y)20( N)-8(a)4(sh equilibria appear in)]TJ /F6 1 Tf -2.81 -1.67 TD 0 Tw (8)Tj /F4 1 Tf 0.97 0 TD 0.001 Tc 0.029 Tw [(. I)14(f)4( )10(the)5( )10(mix)-9(e)5(d)1( )10(stra)5(te)5(g)-9(y)21( )10(is )10(ac)5(tua)5(l)-1(l)-21(y)21( )10(on the)5( )-10(g)11(r)4(id, the)5(n)1( it will be)5( in )]TJ /F7 1 Tf 25.62 0 TD 0 Tc 0 Tw (X)Tj /F4 1 Tf 0.94 0 TD 0.001 Tc 0.029 Tw [(, but this is unlike)5(l)-11(y)31(.)]TJ -27.72 -1.67 TD 0.049 Tw [(I)14(f)-6( the)5( mix)-9(e)5(d)1( stra)5(te)5(g)-9(y)21( is not on the)5( )-10(g)11(r)4(id, there)5( are)5( two )-10(possibilitie)5(s )-10(de)5(pe)5(ndin)-9(g)11( )-10(on )-10(whe)5(t)-1(her)]TJ 0 -1.66 TD 0 Tc 0.04 Tw [(it is stable in the relative best-respons)-11(e d)-20(y)20(namic or not. )-10(I)13(f)-7( it )-10(is )-10(not, )-10(then )-10(there )-10(will )-10(not )-10(be)]TJ 0 -1.67 TD 0.06 Tw [(an)-10(y)20( point in )]TJ /F6 1 Tf 5.4 0 TD 0 Tw (8)Tj /F4 1 Tf 0.97 0 TD 0.07 Tw [( )10(correspondin)-10(g)10( the mix)-10(ed equilibrium. )-10(I)23(f)3( it is stable, then there will be a)]TJ -6.37 -1.67 TD 0.06 Tw [(small cy)20(cl)-12(e around th)-10(e mix)-10(ed equilibrium that will be in )]TJ /F6 1 Tf 23.51 0 TD 0 Tw (8)Tj /F4 1 Tf 0.97 0 TD 0.06 Tw [(\226 it is this we)4( re)4(fe)4(r to a)4(s)-1( the)]TJ -24.48 -1.66 TD 0.001 Tc -0.001 Tw [(mix)-9(e)5(d)1( stra)5(te)5(g)-9(y)21(, a)5(lthou)-9(g)11(h)1( stric)5(t)-1(l)-11(y)21( sp)-9(e)5(a)5(k)1(in)-9(g)11( it is not.)]TJ 3 -1.67 TD -0.001 Tc 0.051 Tw [(The )10(hunter-)-8(g)-1(ather)-8(e)3(r )10(ex)-11(ample )10(re)-7(flects )10(an )-10(aspect of unlikel)-23(y)19( innovation that should)]TJ -3 -1.67 TD 0.001 Tc 0.049 Tw [(be)5( )10(disturbing)11(. )10(There)5( c)5(a)5(n)1( )10(be)5( )10(no stoc)5(h)-9(a)5(stic)5(a)5(l)-1(l)-21(y)21( sta)5(b)1(le)5( mix)-9(e)5(d)1( e)5(quilibria)5(.)1( )-10(I)24(n)1( this e)5(x)-9(a)5(m)-1(ple)5( the)]TJ 0 -1.66 TD 0.079 Tw [(onl)-11(y)21( Na)5(sh )-10(e)5(quilibrium is mi)9(x)-9(e)5(d, a)5(nd the)5( re)5(sult is tha)5(t)-1( the)5( stoc)5(ha)5(stic)5(a)5(l)-1(l)-21(y)21( sta)5(b)1(le)5( )-10(se)5(t )-10(is )-10(not)]TJ 0 -1.67 TD 0.349 Tw [(Na)5(sh )10(a)5(nd g)11(i)-1(ve)5(s )10(pla)-15(y)21(ers )10(le)5(ss )10(tha)5(n)1( )10(the)5( )10(minma)5(x)-9( )10(a)5(s)0( we)5(ll. Howe)5(v)-9(e)5(r, implic)5(it in this)]TJ T* 0 Tc 0.05 Tw [(formulation )10(is )10(that mi)8(x)-10(i)-2(ng)10( takes plac)-6(es b)-20(y)20( ac)-6(cident, throu)-10(g)10(h half o)-10(f)3( the population doing)]TJ 0 -1.66 TD 0.11 Tw [(one )10(thing)10( )10(and )10(h)-10(a)4(lf )10(somethin)-10(g)10( )10(else. )-10(I)13(t)-2( is f)-7(a)4(irl)-12(y)20( )-10(well known in the learning)10( liter)-7(a)4(ture, )-10(for)]TJ 0 -1.67 TD -0.001 Tc 0.111 Tw [(ex)-11(ample )10(from )10(F)5(udenb)-11(er)-8(g)9( )10(and )10(K)-9(r)2(eps )10([)-8(1993])-8(, that this can be problematic. How)-9(e)3(ve)-7(r, we)]TJ T* 0.001 Tc 0.239 Tw [(c)5(a)5(n)1( a)5(l)-1(so c)5(onsider mix)-9(ing)11( )-10(throug)11(h )-20(e)5(x)-9(plic)5(it )-10(ra)5(ndomiza)5(tion: tha)5(t)-1( )-10(is, )-10(introduc)5(e)5( )-10(a)5( )-10(mix)-9(e)5(d)]TJ 0 -1.66 TD -0.001 Tc 0.101 Tw [(strate)-7(g)-11(y)19( as an )-10(ex)-11(plicit pure strateg)-11(y)19(. Suppose th)-11(at we do this )-10(in )-10(the )-10(ex)-11(ample: )-10(we )-10(add )-10(a)]TJ 0 -1.67 TD 0 Tc 0.13 Tw [(strate)-6(g)-10(y)20( )10(of )10(r)-7(a)4(ndomiz)-6(ing)10( )10(50-50 )10(betwe)-6(e)4(n )10(Hunt and G)-8(a)4(ther. )-20(I)23(t)-2( is )-10(appar)-7(e)4(nt that if half the)]TJ T* 0.27 Tw [(population is following)10( this strateg)-10(y)20( )-10(and half is play)10(i)-12(n)-10(g)10( a pu)-10(re str)-7(a)4(te)-6(g)-10(y)20( \(Hunt, fo)-10(r)]TJ 0 -1.66 TD 0.001 Tc 0.039 Tw [(e)5(x)-9(a)5(m)-1(ple)5(\))4( it is be)5(tte)5(r to mi)9(x)-9(.)1( So the)5( ne)5(w mi)9(x)-9(i)-1(ng)11( stra)5(teg)-9(y)21( wins a)5(ll pa)5(irwise)5( conte)5(s)0(ts a)5(nd )-10(is)]TJ 0 -1.67 TD -0.001 Tc 0.001 Tw [(the unique stochasticall)-23(y)19( stable state.)]TJ 3 -1.67 TD 0.001 Tc 0.029 Tw [(Onc)5(e)5( w)-7(e)5( a)5(d)1(mit the)5( possibilit)-11(y)31( o)-9(f)4( e)5(x)-9(plic)5(it mi)9(x)-9(i)-1(ng)11(, howe)5(v)1(e)5(r)4(, there)5( )-10(is )-10(a)5(n)1( )-20(e)5(v)1(e)5(n)1( )-10(be)5(tter)]TJ -3 -1.66 TD -0.001 Tc 0.021 Tw [(idea than c)-7(a)3(n make its wa)-17(y)19( into the )-10(population: )-10(using)9( )-20(a )-10(cor)-8(r)2(elating, )-10(or )-10(identif)-18(y)19(i)-3(n)-11(g)9( )-10(devi)-13(ce.)]TJ ET endstream endobj 117 0 obj << /ProcSet [/PDF /Text ] /Font << /F3 38 0 R /F4 43 0 R /F6 47 0 R /F7 48 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 121 0 obj << /Length 6615 >> stream BT /F3 1 Tf 12 0 0 12 300.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc (11)Tj -17.5 -3 TD 0.18 Tw [(That is, an anon)-20(y)20(m)-2(ous g)10(a)-6(me r)-7(e)4(stricts pla)-16(y)20(e)-6(r)3(s to actions that ar)-7(e independ)-10(ent of )-10(their)]TJ 0 -1.66 TD -0.001 Tc 0.061 Tw [(pla)-7(y)19(e)-7(r)2( )10(roles \(which )10(mi)-13(g)9(h)-1(t )10(corr)-8(espond, )10(for ex)-11(ample, )10(to )10(man and woman\). The)-7( fa)-7(ct is that)]TJ 0 -1.67 TD 0 Tc 0.2 Tw [(while in the laborator)-17(y)20( it is possible to )-10(creat)-12(e )-10(anony)10(m)-12(ous )-10(matchin)-10(g)10( )-20(g)10(a)4(mes, )-10(it )-10(is )-10(not)]TJ T* -0.001 Tc 0.031 Tw [(terribl)-13(y)19( likel)-23(y)19( to happ)-11(en in the field. )-10(I)12(f)-8( the )-10(g)9(a)3(me is pla)-17(y)19(e)-7(d)-1( as a non)-11(-anon)-21(y)19(m)-3(ous )-10(matchin)-11(g)]TJ 0 -1.66 TD 0.111 Tw [(g)9(a)3(m)-13(e)3(, then ther)-8(e ar)-8(e two additional strate)-7(g)9(i)-3(es o)-11(f)2( Hunt when pla)-17(y)19(e)-7(r)2( 1 )-10(and Gathe)-7(r)2( )-10(when)]TJ 0 -1.67 TD -0.002 Tc 0.052 Tw [(pl)-4(a)-8(y)18(e)-8(r)1( 2, and vi)-4(c)-8(e)2( ve)-8(rsa. Ei)-4(t)-4(h)-2(er o)-12(f)1( t)-4(h)-2(ese st)-4(rat)-14(e)-8(g)8(i)-4(es i)-4(s)-3( P)-6(a)2(ret)-4(o)-2( )-10(e)-8(ffi)-4(ci)-4(ent)-4(,)-2( )-10(and )-10(s)-13(eem)-4( )-10(t)-4(o)-2( )-10(re)-8(fl)-4(ect)]TJ T* -0.001 Tc 0.001 Tw [(historical patterns of spec)-7(ializ)-7(ation \(men hunt, women )-10(g)9(a)3(ther)-8(\).)]TJ 3 -1.66 TD 0.071 Tw [(B)6(e)3(c)-7(a)3(use n)-11(e)3(ither of the two n)-11(e)3(w strat)-13(e)-7(g)9(i)-3(es beats the othe)-7(r, it is useful to )-10(consider)]TJ -3 -1.67 TD 0.001 Tc 0.209 Tw [(a)5(n)1( e)5(x)-9(te)5(nsion of the)5( ma)5(in the)5(o)1(re)5(m tha)5(t)-1( )-10(g)11(i)-1(ve)5(s a)5( suffic)5(ie)5(nt )-10(c)5(ondition )-10(for )-20(a)5( )-10(se)5(t )-10(of )-10(pure)]TJ T* -0.001 Tw [(stra)5(teg)11(i)-1(e)5(s)0( to be)5( the)5( onl)-21(y)21( one)5(s re)5(ce)5(iving)11( positive)5( we)5(i)-11(g)11(ht in the)5( limit distribution.)]TJ /F11 1 Tf 0 -2.16 TD 0 Tc 0.09 Tw [(Def)-7(i)-2(nition 4.2:)]TJ /F8 1 Tf 6.21 0 TD [( A set of pure strategies )]TJ /F9 1 Tf 10.62 0.27 TD 0 Tw (e)Tj /F5 1 Tf -0.2 -0.27 TD (3)Tj /F3 1 Tf 0.91 0 TD ( )Tj /F11 1 Tf 0.34 0 TD -0.002 Tc 0.092 Tw [(b)-6(e)2(ats th)-6(e f)-9(i)-4(el)-4(d)]TJ /F8 1 Tf 6.13 0 TD 0.001 Tc 0.089 Tw [( if e)5(a)1(c)5(h)1( )-10(strate)5(gy)5( )]TJ /F9 1 Tf 11.975 0 0 11.975 487.77 501.33 Tm 0 Tc 0 Tw (e)Tj /F5 1 Tf -1.9341 -0.2706 TD 1.323 Tc (S3)Tj /F6 1 Tf 0.7917 0 TD 0 Tc (\211)Tj /F8 1 Tf 12 0 0 12 496.65 498.09 Tm 0.001 Tc [(be)-5(ats)]TJ -33.88 -1.67 TD 0.002 Tc (all )Tj /F9 1 Tf 3.51 0.27 TD 0 Tc (e)Tj /F5 1 Tf -2.04 -0.27 TD 1.419 Tc (S3)Tj /F6 1 Tf 0.85 0 TD 0 Tc (\212)Tj /F10 1 Tf -0.78 0.03 TD (%)Tj /F8 1 Tf 2.69 -0.03 TD (.)Tj /F3 1 Tf -4.23 -2.17 TD [(The nex)-10(t)-2( theorem is specializ)-6(ation of Corollar)-7(y)20( C.2 in App)-10(e)4(ndix)-10( C.)]TJ /F11 1 Tf 0 -2.16 TD -0.001 Tc 0.101 Tw [(Theore)-7(m)12( 4.2:)]TJ /F8 1 Tf 5.81 0 TD 0 Tc 0.1 Tw [( Suppose unlikely innovation, sufficiently large )]TJ /F5 1 Tf 19.81 0 TD 0 Tw (M)Tj /F8 1 Tf 1.16 0 TD 0.001 Tc 0.099 Tw [( and that )]TJ /F9 1 Tf 4.47 0.27 TD 0 Tc 0 Tw (e)Tj /F5 1 Tf -0.2 -0.27 TD (3)Tj /F8 1 Tf 0.91 0 TD 0.001 Tc 0.099 Tw [( b)-9(e)5(ats the)]TJ -31.96 -1.67 TD 0 Tc 0 Tw (field. Then )Tj /T44 1 Tf 8.391 0 0 8.391 176.73 402.69 Tm (e)Tj /F9 1 Tf 12.021 0 0 12.021 189.33 406.05 Tm -0.001 Tc [(\010[)-350(]\011)-1338(\021)]TJ /T45 1 Tf 8.391 0 0 8.391 165.57 400.41 Tm 0.71 Tc (S3)Tj /F5 1 Tf 12.021 0 0 12.021 198.93 406.05 Tm 0 Tc (S)Tj /F7 1 Tf -1.3577 0 TD (N)Tj /T46 1 Tf 8.391 0 0 8.391 169.65 400.41 Tm (\211)Tj /F6 1 Tf 12.021 0 0 12.021 218.25 406.05 Tm (\036)Tj 18.031 0 0 18.031 150.21 403.29 Tm (\234)Tj /F8 1 Tf 12 0 0 12 239.49 406.05 Tm (.)Tj -12.45 -2.17 TD -0.001 Tc 0.001 Tw (Proof: )Tj /F3 1 Tf 3.11 0 TD 0 Tc 0 Tw [(See Appendix)-10( C, L)11(e)4(mma C.2 \(i\).)]TJ /F12 1 Tf 32 -1.66 TD (\346)Tj /F3 1 Tf -32.11 -1.67 TD -0.002 Tc 0.122 Tw [(Turni)-4(n)-2(g)8( b)-12(ack t)-4(o)-2( t)-4(h)-2(e ex)-12(am)-4(pl)-4(e, we s)-13(ee t)-4(h)-2(at)-4( Hunt)-4(/)-4(G)0(at)-4(h)-12(e)2(r and G)-10(a)2(t)-4(h)-2(er/)-4(H)0(unt)-4( )-10(are t)-4(h)-2(e)]TJ -3 -1.67 TD 0.001 Tc -0.001 Tw [(stoc)5(ha)5(stic)5(a)5(l)-1(l)-11(y)21( sta)5(b)1(l)-11(e)5( se)5(t; it is c)5(l)-1(e)5(a)5(r)4( from s)-10(y)21(mme)5(tr)-16(y)21( th)-9(a)5(t)-1( the)-15(y)21( a)5(r)-6(e)5( e)5(qua)5(ll)-21(y)21( like)5(l)-1(y)11(.)]TJ 3 -1.66 TD 0.009 Tw [(Compa)5(r)4(ison to the)5( sta)5(nda)5(rd c)5(a)5(s)-10(e)5( is simplifie)5(d if we)5( brea)5(k part )-10(of )-10(the)5( )-10(s)-20(y)31(mm)-11(e)5(t)-1(r)-16(y)21( )-10(b)-19(y)]TJ -3 -1.67 TD 0 Tc 0.03 Tw [(supposing)10( )10(that )10(Gather/Gather is safer, and ther)-7(efore a little better than )-10(Hunt/Hunt, so that)]TJ T* -0.001 Tc 0.001 Tw [(the pa)-17(y)19(o)-1(ffs a)-7(r)2(e)]TJ /F11 1 Tf 4.46 -3.34 TD 0.004 Tc [(Hunt)-1333(G)12(a)4(t)7(h)0(e)8(r)]TJ ET 1 i 137.85 236.01 0.6 -19.92 re f 180.69 236.01 0.6 -19.92 re f BT 12 0 0 12 90.09 199.17 Tm (Hunt)Tj /F3 1 Tf 4.46 0 TD 0 Tc [(0,0)-2320(1,1)]TJ ET 84.69 215.97 53.04 -0.6 re f 137.85 215.97 0.6 -0.6 re f 138.57 215.97 42 -0.6 re f 180.69 215.97 0.6 -0.6 re f 181.41 215.97 53.04 -0.6 re f 137.85 215.25 0.6 -19.92 re f 180.69 215.25 0.6 -19.92 re f BT /F11 1 Tf 12 0 0 12 90.09 178.41 Tm -0.005 Tc [(Ga)-5(th)-9(er)]TJ /F3 1 Tf 4.46 0 TD 0 Tc [(1,1)-2320(1/4,1/4)]TJ ET 84.69 195.21 53.04 -0.6 re f 137.85 195.21 0.6 -0.6 re f 138.57 195.21 42 -0.6 re f 180.69 195.21 0.6 -0.6 re f 181.41 195.21 53.04 -0.6 re f 137.85 194.49 0.6 -19.92 re f 180.69 194.49 0.6 -19.92 re f BT 12 0 0 12 90.09 138.57 Tm -0.001 Tc 0.151 Tw [(This )10(does )10(not )10(chan)-11(g)9(e)3( the a)-7(n)-1(al)-23(y)19(s)-2(is in the cas)-12(e of unlikel)-23(y)19( innovation. Howeve)-7(r, in the)]TJ /F4 1 Tf 0 -1.67 TD 0.141 Tw [(standard an)-11(al)-13(y)19(s)-2(is \275 dominanc)-7(e)3( fails. To se)-7(e this observe that )-10(if )-10(h)-11(a)3(lf )-10(the )-10(population )-10(is)]TJ T* 0 Tc 0.12 Tw [(pla)-6(y)20(in)-10(g)10( )10(Hunte)-6(r)3(/Gathe)-6(r )10(and )10(half is pla)-16(y)20(in)-10(g)10( G)-8(a)4(ther/Hunt the b)-10(e)4(st response is Hunt/Hunt,)]TJ 0 -1.66 TD 0.04 Tw [(that )10(is )10(neither )10(of the two. Despite this, we )-10(can us)-11(e Ellison [)-7(1995])-7(\222s methods t)8(o)0( show that)]TJ ET endstream endobj 122 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F3 38 0 R /F4 43 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F10 61 0 R /F11 62 0 R /F12 90 0 R /T44 123 0 R /T45 124 0 R /T46 125 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 126 0 obj << /Length 6979 >> stream BT /F3 1 Tf 12 0 0 12 300.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc (12)Tj -17.5 -3 TD -0.001 Tc 0.221 Tw [(Hunt/Gather )10(and Gather/Hunt are )10(the uniqu)-11(e stochasticall)-23(y)19( stable s)-12(e)3(t in the standard)]TJ 0 -1.66 TD 0.001 Tc 0.219 Tw [(mode)5(l. The)5(r)4(e)5( )-10(a)5(r)4(e)5( ma)5(n)-19(y)21( mix)-9(e)5(d)1( e)5(quilibria)5( of this mode)5(l, )-10(but )-10(a)5(dding)11( )-10(on)-9(e)5( )-10(Hunt/Ga)5(t)-1(her)]TJ 0 -1.67 TD -0.001 Tc 0.021 Tw [(innovation to one of these equilibria causes Hunt/Gath)-11(e)3(r to becom)-13(e)3( the best r)-8(e)3(sponse )-10(and)]TJ T* 0.361 Tw [(vice vers)-12(a, while it takes quite a f)-8(e)3(w innovations )-10(to )-20(g)9(e)3(t )-10(out )-10(of )-10(Hunt/Gathe)-7(r )-10(or)]TJ 0 -1.66 TD 0 Tc [(Ga)4(the)4(r)3(/Hunt.)]TJ /F1 1 Tf 14.04 0 0 14.04 90.09 592.05 Tm 0.004 Tw [(5. )-9(A)64( Gif)25(t)8( G)9(i)-4(v)9(i)-4(ng Game)]TJ /F3 1 Tf 12 0 0 12 126.09 569.01 Tm 0.001 Tc 0.159 Tw [(We)5( now c)5(onside)5(r)4( a)5( more)5( e)5(x)-9(te)5(nde)5(d )-10(e)5(x)-9(a)5(m)-1(ple)5(.)1( )-10(The)5( )-10(se)5(ttin)-9(g)11( )-10(is )-10(a)5( )-20(g)11(i)-1(ft-g)11(i)-11(v)1(ing)11( )-20(ga)5(me)]TJ -3 -1.66 TD 0 Tc 0.21 Tw [(introduced b)-20(y)20( J)-11(ohnson, )-10(L)21(e)4(vine )-10(and Pesendor)-7(fer [)-7(1999])-7( to stud)-10(y)30( th)-10(e evolution )-10(of )-10(the)]TJ 0 -1.67 TD 0.33 Tw [(social )10(norm )10(of )10(coope)-6(ration. )-10(I)13(n)0( this )-10(g)10(a)4(me pla)-16(y)20(e)-6(r)3(s live two pe)-6(riods in overlappin)-10(g)]TJ T* 0.01 Tw [(g)10(e)4(n)-10(e)4(rations. )10(Youn)-10(g)10( )10(pla)-16(y)20(e)-6(r)3(s a)-6(r)3(e r)-7(a)4(ndoml)-12(y)20( m)-12(a)4(tched a)-6(g)0(ainst an equ)-10(a)4(l number of old pla)-16(y)20(e)-6(r)3(s)]TJ 0 -1.66 TD -0.001 Tc 0.091 Tw [(and must choose whethe)-7(r to g)9(i)-3(v)-11(e)3( or withhold a )-10(g)9(i)-3(ft from the old oppon)-11(ent. Old pla)-17(y)19(ers)]TJ 0 -1.67 TD 0.041 Tw [(are )10(passive and )10(do )10(not )10(have )-10(an a)-7(c)3(tion. Howeve)-7(r, the beh)-11(a)3(vior when )-20(y)19(oun)-11(g)9( is r)-8(e)3(ported on)]TJ T* 0.01 Tc [(by)30( )]TJ /F8 1 Tf 1.28 0 TD 0.001 Tc 0.039 Tw [(information sy)5(ste)5(m)3(s)]TJ /F3 1 Tf 8.07 0 TD -0.001 Tc 0.041 Tw [( so they)9( )-10(ma)-17(y)19( b)-11(e)3( rew)-9(a)3(rd or punish)-11(ed based on )-10(what the)-17(y)19( did when)]TJ -9.35 -1.66 TD 0 Tc 0.18 Tw [(the)-6(y)20( w)-8(e)4(re )-20(y)20(o)0(u)-10(n)-10(g)10(. This is a variation on the model )-10(of )-10(Ka)-6(ndori )-10([)-7(1992])-7(, )-10(and )-10(following)]TJ /F4 1 Tf 0 -1.67 TD -0.001 Tc 0.241 Tw [(Kandori, it is possible to prove a folk theor)-8(e)3(m for this model if )-10(there )-10(is )-10(\223en)-11(ou)-11(g)9(h)-1(\224)]TJ T* 0 Tc 0 Tw [(information about old play)10(e)-6(r)3(s.)]TJ 3 -1.66 TD 0.03 Tw [(Spe)4(c)4(i)-2(fic)4(a)4(l)-2(l)-22(y)20(, )10(we)4( a)4(ssume)4( )10(tha)4(t)-2( )10(it )10(c)4(o)0(sts the)4( )-10(y)20(oun)-10(g)10( pl)-12(a)4(y)10(er 1 unit of utilit)-12(y)20( fo)-10(r )-10(g)10(i)-2(ving)10( )-10(a)]TJ -3 -1.67 TD -0.001 Tc 0.021 Tw [(g)9(i)-3(ft, and p)-11(r)2(ovides a ben)-11(e)3(fit )-10(of )]TJ /F9 1 Tf 11.97 0 0 11.97 263.37 349.05 Tm 0 Tc 0 Tw (\021)Tj /F7 1 Tf -2.0251 0 TD (B)Tj /F6 1 Tf 0.9725 0 TD (\037)Tj /F4 1 Tf 12 0 0 12 271.77 349.05 Tm 0.001 Tc 0.029 Tw [( to the)5( olde)5(r rec)5(i)-1(pie)5(n)1(t. Pay)21(o)-9(ffs are)5( a)5(dditive)5( b)-9(e)5(twe)5(e)5(n)]TJ -15.14 -1.67 TD 0 Tc 0.03 Tw [(the)4( two pe)4(riods of life)4( so tha)4(t)-2( gift-givin)-10(g)10( is e)4(f)-7(fic)4(i)-2(e)4(n)0(t. )-10(Note)4( )-10(the)4( )-20(re)4(se)4(mbla)4(n)-10(c)4(e)4( )-10(of )-10(the)4( )-10(mod)-10(e)4(l)]TJ 0 -1.66 TD 0.01 Tw [(to Prisoners')10( Dilemma. Th)-10(e m)-12(y)20(opi)-12(c optimum for the )-20(y)20(oun)-10(g)10( pla)-16(y)20(er is )-10(to )-10(withhold )-10(the )-10(g)10(i)-2(ft,)]TJ 0 -1.67 TD 0.04 Tw [(just a)4(s)-1( de)4(fe)4(c)4(tion is domina)4(n)0(t whe)4(n)0( the)4( Prisone)4(rs)-11(\222 Dile)4(mma)4( is pla)-16(y)20(e)4(d)0( on)-10(c)4(e)4(.)0( )-10(How)-8(e)4(ve)4(r, )-10(th)-10(e)]TJ T* -0.001 Tc 0.271 Tw [(overlappin)-11(g)9( g)9(e)3(ne)-7(rations )10(environment allows )10(for )10(a c)-7(onnection betw)-9(een )-10(actions when)]TJ 0 -1.66 TD 0 Tc 0.13 Tw [(y)20(o)-10(un)-10(g)10( )10(a)4(nd p)-10(a)-16(y)20(o)0(ffs )-10(whe)4(n)0( old, just a)4(s)-1( re)4(p)-10(e)4(titions would a)4(llow for c)4(onse)4(q)0(u)-10(e)4(nc)4(e)4(s)-1( in la)4(ter)]TJ 0 -1.67 TD -0.001 Tc 0.001 Tw [(periods to influence )-10(earlie)-7(r actions in a r)-8(e)3(pe)-7(ated Prisoners)-12(')9( Dilemma.)]TJ 3 -1.67 TD 0.131 Tw [(The)-7(y)19( k)-11(e)-17(y)19( assum)-3(p)-1(t)-3(i)-3(on i)-3(s)-2( t)-3(h)-1(at)-3( enabl)-3(e)3(s )-10(coop)-11(er)-8(at)-3(i)-3(v)-1(e )-10(pl)-3(a)-17(y)19( )-10(i)-3(s)-2( )-10(t)-3(h)-1(at)-3( )-20(y)19(oun)-11(g)9( )-10(pl)-13(a)-17(y)19(ers )-20(are)]TJ -3 -1.66 TD 0 Tc 0.06 Tw [(\(partiall)-22(y)20(\))3( )10(informed about )10(the )10(histor)-17(y)20( )10(of their olde)-6(r opponent. F)6(o)0(llowin)-10(g)10( Kan)-10(dori [)-7(1992])]TJ 0 -1.67 TD 0.14 Tw [(we)4( mode)4(l this throug)10(h )]TJ /F8 1 Tf 9.77 0 TD 0.001 Tc 0.149 Tw [(information sy)5(ste)5(m)3(s)]TJ /F4 1 Tf 8.18 0 TD -0.001 Tc 0.151 Tw [(. An info)-11(rmation s)-12(y)19(stem p)-11(r)2(ovides a si)-13(g)9(n)-1(al)]TJ -17.95 -1.67 TD 0.191 Tw [(about )10(past )10(pla)-7(y)19(. )10(W)-7(e)3( ex)-11(amine )10(the )10(simplest case in which this sig)9(n)-1(al )-10(can tak)-11(e)3( on two)]TJ 0 -1.66 TD -0.002 Tc 0.012 Tw [(val)-4(u)-2(es, whi)-4(c)2(h w)-10(e)2( desc)-8(ri)-4(be as a )-10(\223red )-10(fl)-4(a)-8(g)8(\224 o)-12(r)1( a \223gr)-9(e)2(e)-8(n)-2( fl)-4(a)-8(g)8(.\224 )-10(L)9(e)-8(t)-4( )]TJ /F3 1 Tf 26.01 0 TD 0.4 Tc [({,)-240(})]TJ ET q 1 i 407.37 139.05 4.68 -12.84 re W* n BT /F8 1 Tf 12 0 0 12 407.37 129.09 Tm 0 Tc 0 Tw (r)Tj ET Q BT /F8 1 Tf 12 0 0 12 417.69 129.09 Tm 0 Tc 0 Tw (g)Tj /F4 1 Tf 1.11 0 TD 0.001 Tc 0.009 Tw [( be)5( the)5( se)5(t of flag)11(s.)]TJ -28.41 -1.67 TD -0.002 Tc 0.112 Tw [(Form)-4(al)-4(l)-24(y)18(, an )]TJ /F8 1 Tf 5.57 0 TD 0.001 Tc 0.109 Tw [(information sy)5(ste)5(m)]TJ /F4 1 Tf 7.75 0 TD [( is a)5( ma)5(p )]TJ /F3 1 Tf 11.97 0 0 11.97 306.93 109.05 Tm 0.213 Tc -0.012 Tw [( : )220({)272(0)232(,)192(1)332(})-570({)-179(,)-459(})-1061({)-179(,)-469(})]TJ /F8 1 Tf -0.3509 0 TD 4.514 Tc [(ir)4071(g)2287(r)4081(g)]TJ ET q 1 i 346.77 119.97 60.84 -14.4 re W* n BT /F14 1 Tf 11.97 0 0 11.97 346.77 109.05 Tm 2.527 Tc (\234\226)Tj ET Q BT /F4 1 Tf 12 0 0 12 425.25 109.05 Tm 0 Tc 0.11 Tw [( that assig)10(n)0(s )-20(an )-10(old)]TJ -27.93 -1.67 TD -0.001 Tc 0.101 Tw [(pla)-7(y)19(e)-7(r)2( a )-10(fla)-7(g)9( based on his own )-10(action \(the siz)-7(e)3( of the )-10(g)9(i)-3(ft \226 0 or )-10(1)-11(\))2( )-10(and )-10(the )-20(fla)-7(g)9( )-10(of )-10(the)]TJ ET endstream endobj 127 0 obj << /ProcSet [/PDF /Text ] /Font << /F1 36 0 R /F3 38 0 R /F4 43 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F14 128 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 130 0 obj << /Length 11707 >> stream BT /F3 1 Tf 12 0 0 12 300.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc (13)Tj -17.5 -3 TD -0.001 Tc 0.051 Tw [(opponent )10(he )10(met when )-20(y)19(oun)-11(g)9(.)-1( )-20(I)22(t)-3( is e)-7(a)3(sil)-13(y)19( )-10(check)-11(ed that ther)-8(e ar)-8(e 16 information s)-22(y)19(stems.)]TJ 0 -1.66 TD 0.191 Tw [(W)-7(e)3( denote the set of inform)-13(ation s)-12(y)19(stems b)-21(y)19( )]TJ /F8 1 Tf 19.63 0 TD -0.003 Tc (I )Tj /F3 1 Tf 0.78 0 TD 0 Tc [(a)-6(nd )]TJ /F8 1 Tf 7 0 0 7 365.85 681.09 Tm 0 Tw (i)Tj 12 0 0 12 362.01 684.09 Tm (f)Tj /F3 1 Tf 0.66 0 TD -0.001 Tc 0.201 Tw [( for the fla)-7(g)9( co)-11(rresponding to)]TJ -23.32 -1.67 TD 0.001 Tw (information service )Tj /F8 1 Tf 8.04 0 TD 0 Tc 0 Tw (i)Tj /F3 1 Tf 0.28 0 TD (.)Tj -5.32 -1.67 TD 0.09 Tw [(F)6(l)-2(a)-6(g)10( ve)-6(ctors )]TJ /F5 1 Tf 5.62 0 TD 0 Tw (F)Tj /F3 1 Tf 0.73 0 TD -0.001 Tc 0.101 Tw [( )10(correspondin)-11(g)9( )10(to the diffe)-7(rent information s)-22(y)19(stems a)-7(r)2(e obse)-7(r)2(ved)]TJ -9.35 -1.66 TD 0 Tc 0.07 Tw [(b)-10(y)20( )-10(y)20(oun)-10(g)10( )10(opponents as follows. With probabilit)-12(y)30( )]TJ 11.97 0 0 11.97 334.17 624.09 Tm 0 Tw (1)Tj ET q 1 i 348.93 635.01 9.6 -14.4 re W* n BT /F15 1 Tf 11.97 0 3.699 11.97 348.93 624.09 Tm (h)Tj ET Q BT /F15 1 Tf 11.97 0 0 11.97 341.49 624.09 Tm (-)Tj /F3 1 Tf 12 0 0 12 358.53 624.09 Tm -0.001 Tc 0.071 Tw [( the fla)-7(g)9( ve)-7(ctor observ)-11(e)3(d is equal)]TJ -22.37 -1.67 TD 0 Tc 0.11 Tw [(to the)4( ve)4(c)4(t)-2(or a)4(ssi)-12(g)10(n)0(e)4(d)0( b)-20(y)20( the)4( di)-12(ffere)4(nt informa)4(tion s)-21(y)20(ste)4(m)-2(s. With proba)4(bilit)-12(y)30( )]TJ 11.97 0 0 11.97 495.45 604.05 Tm 0 Tw (0)Tj ET q 1 i 475.53 614.97 24 -14.4 re W* n BT /F15 1 Tf 11.97 0 3.699 11.97 475.53 604.05 Tm (h)Tj ET Q BT /F15 1 Tf 11.97 0 0 11.97 486.09 604.05 Tm (>)Tj /F3 1 Tf 12 0 0 12 503.13 604.05 Tm 0.001 Tc 0.109 Tw [( the)]TJ -34.42 -1.67 TD -0.001 Tc 0.061 Tw [(flag)9( v)-11(ector obs)-12(erved is chos)-12(en randoml)-23(y)19( a)-7(cco)-11(rding)9( to )-10(a uniform distribution on )]TJ /F8 1 Tf 32.84 0 TD 0 Tc 0 Tw (F)Tj /F3 1 Tf 0.9 0 TD 0.06 Tw [(. W)-6(e)]TJ -33.74 -1.66 TD -0.001 Tc 0.121 Tw [(assume that the chan)-11(ce )-10(a pla)-17(y)19(er is assi)-13(g)9(n)-1(ed a )-10(r)-8(a)3(ndom )-10(flag)9( )-10(vector )-10(is )-10(small: )-10(specificall)-23(y)]TJ 0 -1.67 TD 0.001 Tc [(tha)5(t)-1( )]TJ 11.97 0 0 11.97 123.45 544.05 Tm 1.436 Tc [(:\()1488(1)31(\))496(1)]TJ ET q 1 i 113.25 554.97 72.84 -14.4 re W* n BT /F15 1 Tf 11.97 0 3.699 11.97 113.25 544.05 Tm 0 Tc 0 Tw (b)Tj ET Q BT /F15 1 Tf 11.97 0 3.699 11.97 135.21 544.05 Tm 1.615 Tc (ah)Tj 11.97 0 0 11.97 126.57 544.05 Tm 1.797 Tc [(=-)491(>)]TJ /F3 1 Tf 12 0 0 12 192.09 544.05 Tm 0 Tc 0 Tw (.)Tj -5.5 -1.67 TD 0.02 Tw [(F)6(i)-2(nall)-12(y)20(,)0( )-10(we assume th)-10(at a )-20(y)20(oun)-10(g)10( pla)-16(y)20(e)-6(r)3( ma)-16(y)20( )-10(consult )-10(onl)-22(y)20( )-10(one )-10(information )-10(s)-21(y)20(stem.)]TJ -3 -1.66 TD -0.002 Tc 0.022 Tw [(Thi)-4(s)-3( m)-4(eans t)-4(h)-2(at)-4( t)-4(h)-2(e onl)-14(y)18( f)-9(easi)-4(b)-2(l)-4(e)2( st)-4(r)-9(a)2(t)-4(e)-8(g)8(i)-4(es a)-8(r)1(e t)-4(hose of t)-4(h)-12(e form)-4( )]TJ 11.97 0 0 11.97 424.77 504.09 Tm 0.569 Tc [(\(,)157(\))]TJ /F8 1 Tf -1.4336 0 TD 1.416 Tc [(sa)1054(i)]TJ /F14 1 Tf 0.653 0.0017 TD 0 Tc 0 Tw (=)Tj /F3 1 Tf 12 0 0 12 449.61 504.09 Tm 0.001 Tc 0.019 Tw [( c)5(onsists of )-10(the)]TJ -29.96 -1.67 TD -0.002 Tc 0.222 Tw (choice of )Tj /F8 1 Tf 4.37 0 TD 0 Tc [(on)-10(e)]TJ /F3 1 Tf 1.45 0 TD 0.22 Tw [( information s)-21(y)20(stem )]TJ /F8 1 Tf 11.963 0 0 11.963 268.41 484.05 Tm 1.056 Tc (iI)Tj /F14 1 Tf 0.5116 0 TD 0 Tc 0 Tw (\266)Tj /F3 1 Tf 12 0 0 12 291.93 484.05 Tm -0.001 Tc 0.221 Tw [( and a map )]TJ ET q 1 i 368.01 494.85 72.96 -13.68 re W* n BT 11.97 0 0 11.97 368.01 484.05 Tm 0.113 Tc [(:{)-279(,)-559(})-1161({)162(0)132(,)92(1)232(})]TJ ET Q BT /F8 1 Tf 11.97 0 0 11.97 359.61 484.05 Tm 1.044 Tc [(ar)601(g)]TJ /F14 1 Tf 3.5001 0.0016 TD 0 Tc 0 Tw (\226)Tj /F3 1 Tf 12 0 0 12 440.97 484.05 Tm -0.001 Tc 0.231 Tw [( that assig)9(n)-1(s an)]TJ -29.24 -1.67 TD 0.001 Tw [(action to a fla)-7(g)9(.)]TJ 3 -1.66 TD 0.001 Tc 0.079 Tw [(F)7(i)-1(na)5(ll)-11(y)21(,)1( )-10(we)5( must spe)5(c)5(i)-1(f)-16(y)21( ho)-9(w e)5(x)-9(pe)5(c)5(t)-1(e)5(d)1( utilit)-11(y)21( )]TJ /F9 1 Tf 19.78 0 TD 0.33 Tc [(\010\014)-370(\011)]TJ ET q 1 i 356.85 456.09 33.96 -18 re W* n BT /F5 1 Tf 12 0 0 12 356.85 444.09 Tm 0.32 Tc (US)Tj ET Q BT /F7 1 Tf 12 0 0 12 376.77 444.09 Tm 0 Tc 0 Tw (T)Tj /F3 1 Tf 1.17 0 TD 0.001 Tc 0.089 Tw [( is de)5(te)5(rmine)5(d. Utilit)-11(y)21( to a)]TJ -25.06 -1.67 TD -0.001 Tc 0.001 Tw [(y)19(o)-11(un)-11(g)9( pla)-17(y)19(e)-7(r)2( dep)-11(e)3(nds on ex)-11(pectations )-10(of )-10(futur)-8(e)3( )-10(play)9( )-20(b)-21(y)19( )-10(nex)-11(t)-3( )-10(period )-20(y)19(oun)-11(g)9( )-10(pl)-13(a)-17(y)19(ers )]TJ /F7 1 Tf 33.42 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 0.88 0 TD -0.002 Tc 0.012 Tw [( and)]TJ -34.3 -1.67 TD -0.001 Tc 0.141 Tw [(on the distribution of flag)9(s amon)-11(g)9( )-10(curr)-8(ent old pla)-7(y)19(e)-7(r)2(s. As usual, )-10(we take th)-11(e previous)]TJ 0 -1.66 TD 0 Tc 0.12 Tw [(period distribution of )-10(strate)-6(g)10(i)-2(es )]TJ /T47 1 Tf 8.355 0 0 8.355 268.05 380.13 Tm 0 Tw (\021)Tj /T48 1 Tf -1.1633 0 TD (T)Tj /F7 1 Tf 11.97 0 0 11.97 251.85 384.09 Tm (T)Tj /T49 1 Tf 8.355 0 0 8.355 261.93 380.13 Tm (\016)Tj /F3 1 Tf 12 0 0 12 274.41 384.09 Tm -0.001 Tc 0.131 Tw [( as a prox)-21(y)19( for b)-11(e)3(liefs about ex)-11(pectations of n)-11(e)3(x)-11(t)]TJ -15.36 -1.67 TD 0 Tc 0.01 Tw [(period pla)-16(y)20(. W)-6(e)4( furthe)-6(r assume that the distribution of cur)-7(r)3(ent old pla)-16(y)20(er )-10(flags )-10(is )-10(believed)]TJ T* -0.002 Tc 0.332 Tw [(t)-4(o)-2( be t)-4(h)-2(e st)-4(ead)-22(y)18( st)-4(at)-4(e di)-4(st)-4(ri)-4(but)-4(i)-4(o)-2(n)]TJ 8.04 0 0 8.04 268.17 349.53 Tm 0.006 Tc (5,6)Tj 12 0 0 12 278.37 344.01 Tm -0.001 Tc [( of flag)9(s cor)-8(r)2(espondin)-11(g)9( )-10(to )]TJ /T47 1 Tf 8.355 0 0 8.355 443.25 340.05 Tm 0 Tc 0 Tw (\021)Tj /T48 1 Tf -1.1633 0 TD (T)Tj /F7 1 Tf 11.97 0 0 11.97 427.05 344.01 Tm (T)Tj /T49 1 Tf 8.355 0 0 8.355 437.13 340.05 Tm (\016)Tj /F3 1 Tf 12 0 0 12 449.61 344.01 Tm -0.001 Tc 0.341 Tw [( being)9( pla)-7(y)19(ed)]TJ -29.96 -1.66 TD 0.001 Tc 0.019 Tw [(re)5(pe)5(a)5(t)-11(e)5(d)1(l)-11(y)21(. Since)5( a)5(ll flag)11( vec)5(t)-1(ors ha)5(v)-9(e)5( positive)5( proba)5(bilit)-11(y)21(,)1( )-10(this )-10(ste)5(a)5(d)-19(y)21( )-10(sta)5(t)-1(e)5( )-10(is )-10(unique)5( )-20(a)5(n)1(d)]TJ 0 -1.67 TD -0.001 Tc 0.251 Tw [(we )10(denote )10(the corr)-8(esponding)9( m)-13(a)3(r)-8(g)9(inal prob)-11(abilit)-13(y)19( distribution over )]TJ /F5 1 Tf 29.27 0 TD 0 Tc 0 Tw (&)Tj /F3 1 Tf 1.06 0 TD 0.01 Tc 0.24 Tw [( by)30( )]TJ /T50 1 Tf 8.355 0 0 8.355 507.57 300.09 Tm 0 Tc 0 Tw (\021)Tj /F9 1 Tf 11.975 0 0 11.975 487.05 304.05 Tm 1.714 Tc (\010\011)Tj /T51 1 Tf 8.355 0 0 8.355 497.85 300.09 Tm 0 Tc (T)Tj /F7 1 Tf 11.975 0 0 11.975 480.33 304.05 Tm 0.331 Tc (GT)Tj /T52 1 Tf 8.355 0 0 8.355 501.45 300.09 Tm 0 Tc (\016)Tj /F3 1 Tf 12 0 0 12 519.09 304.05 Tm (.)Tj -35.75 -1.67 TD 0.001 Tc -0.001 Tw [(Ex)-9(pe)5(c)5(t)-1(e)5(d)1( utilit)-11(y)31( is the)5(n)1( c)5(a)5(l)-11(c)5(u)1(la)5(te)5(d with re)5(spe)5(c)5(t)-1( to )]TJ /F7 1 Tf 20.13 0 TD 0 Tc 0 Tw (G)Tj /F3 1 Tf 0.89 0 TD (.)Tj -18.02 -1.66 TD 0.001 Tc 0.109 Tw [(We)5( )10(a)5(r)4(e)5( g)11(o)1(in)-9(g)11( )10(to foc)5(u)1(s on two ke)-15(y)21( t)-21(y)21(p)-9(e)5(s of stra)5(teg)11(i)-1(es. One)5( is the)5( )]TJ /F8 1 Tf 27.3 0 TD [(alway)5(s)0( se)5(lfish)]TJ /F4 1 Tf -30.3 -1.67 TD -0.001 Tc 0.001 Tw [(strate)-7(g)-11(y)19( of makin)-11(g)9( a low tr)-8(ansfe)-7(r)2( re)-7(gardless of th)-11(e old )-10(opponent\222s )-10(fla)-7(g)9( )-10(v)-11(ector. )-10(Th)-11(e )-10(second)]TJ T* 0.001 Tc 0.179 Tw [(t)-11(y)21(pe)5( of st)-11(ra)5(teg)-9(y)21( w)-7(e)5( c)5(onside)5(r)4( is )-10(e)5(x)-9(e)5(m)-1(plifie)5(d )-10(b)-9(y)21( )-10(the)5( )]TJ /F8 1 Tf 21.83 0 TD -0.001 Tc [(gre)-7(e)3(n-team)]TJ /F4 1 Tf 4.55 0 TD 0.002 Tc 0.188 Tw [( stra)6(teg)-8(y)22(. This use)6(s)1( a)6(n)]TJ -26.38 -1.66 TD -0.002 Tc 0.042 Tw [(i)-4(n)-2(form)-4(at)-4(i)-4(on )10(s)-13(y)18(st)-4(em)-4( )10(t)-4(h)-2(at)-4( )10(assi)-14(g)8(n)-2(s )10(a green )-10(fl)-4(a)-8(g)8( t)-4(o)-2( hi)-4(g)8(h)-2( t)-14(r)1(ansf)-9(er a)-8(g)-2(ai)-4(nst)-4( a gre)-8(e)2(n fl)-4(a)-8(g)8( and l)-4(o)-2(w)]TJ 0 -2.05 TD 0 Tc 0 Tw ( )Tj ET 1 i 90.09 182.61 143.88 -0.48 re f BT /F3 1 Tf 6.48 0 0 6.48 90.09 171.09 Tm (5)Tj 9.96 0 0 9.96 93.33 166.53 Tm -0.001 Tc 0.233 Tw [( )12(T)-17(h)5(is )12(lo)-7(ng ru)-7(n v)-7(i)0(e)-15(w)10( o)-7(f)7( t)-12(h)5(e f)7(l)0(a)-15(g)5( d)-7(i)0(strib)-19(u)5(tio)-7(n )-12(m)6(a)-15(y)17( )-12(see)-15(m)18( )-12(inco)-19(nsis)-10(ten)-7(t)0(, b)-7(u)5(t the o)-19(v)5(erlap)-7(p)-7(i)0(ng ge)-15(nerat)-12(i)0(o)-7(n)5(s)]TJ -0.3253 -1.1566 TD 0.002 Tc 0.061 Tw [(stru)8(ct)-9(u)8(r)-2(e )12(does )12(n)8(o)-4(t m)21(e)0(a)-12(n)8( )12(th)8(a)-12(t)3( )12(each)8( )12(pla)-12(y)20(er )12(on)8(l)-9(y)8( )12(pla)-12(y)8(s on)8(ce, )-12(m)9(e)0(rel)-9(y)20( t)-9(h)8(at i)-9(n)8(f)10(o)-4(r)-14(m)9(ation)8( abou)8(t play)8( o)-16(n)8(l)-9(y)20( persi)-9(s)5(ts)]TJ T* 0.004 Tc -0.001 Tw [(f)12(o)-2(r a s)7(i)5(ng)10(l)5(e)2( peri)5(od.)]TJ 6.48 0 0 6.48 90.09 136.53 Tm 0 Tc 0 Tw (6)Tj 9.96 0 0 9.96 93.33 131.97 Tm 0.087 Tw [( If)8( b)-6(e)-2(lief)8(s)3( ab)-6(o)-6(u)6(t )-12(f)8(l)1(a)-14(g)6( d)-6(i)1(strib)-6(u)6(t)-11(i)1(o)-6(n)6(s are no)-6(i)-11(s)-9(y)18( t)-11(h)6(i)-11(s)3( )-12(w)11(ill e)-14(f)8(f)8(ect res)-9(u)6(lt)-11(s. Ho)-18(w)11(e)-2(ver, as t)-11(h)6(eo)-6(rists )-12(w)11(e)-2( are lo)-6(o)-6(k)6(i)-11(n)6(g)]TJ /F4 1 Tf -0.3253 -1.1566 TD -0.001 Tc 0.076 Tw [(f)7(o)-7(r si)-12(m)18(p)-7(le case)-15(s)2( to)-7( b)-7(u)5(ild)-7( q)-7(u)5(alitat)-12(i)0(ve i)-12(n)5(t)-12(u)5(itio)-19(n \226)-7( nu)-7(m)6(e)-3(rical )-12(a)-15(n)5(al)-12(ysis )-12(req)-7(u)-7(i)0(res )-12(si)-12(m)6(u)-7(latio)-7(n)-7(s)2(. )-12(Our )-24(f)7(o)-7(cus )-24(here )-12(is)]TJ T* 0.028 Tw [(o)-7(n)5( )12(ro)-7(le )12(o)-7(f)7( )12(i)-12(m)18(itatio)-19(n )12(in )12(p)-7(r)-5(o)-7(p)-7(a)-3(gatio)-7(n so)-7( )-12(w)22(e)-3( d)-7(o)-7( no)-7(t cho)-7(o)-7(s)2(e to)-7( let it co)-19(m)18(p)-7(ete )-12(w)10(i)0(t)-12(h)5( o)-7(t)0(her so)-19(urces o)-7(f)7( rand)-7(o)-19(m)6(ne)-15(ss.)]TJ 0 -1.1446 TD 0.002 Tc 0.085 Tw [(T)-14(h)8(e )12(assum)21(p)-16(tion)8( )12(t)-9(h)8(at )12(flag)8( )12(dis)-7(t)3(ribu)8(tion)8( )12(are )12(stead)-16(y)8( state are on)8(ly)8( o)-16(n)8(e of)10( )-12(m)9(a)-12(ny)20( )-12(su)8(c)-12(h)8( si)-9(m)9(p)-4(li)-9(fy)8(ing)8( as)-7(sum)9(p)-4(tio)-16(n)8(s)]TJ 0 -1.1566 TD -0.001 Tc 0.305 Tw [(stand)-7(a)-3(rd)-7( )12(in )12(t)-12(h)5(eo)-7(retical )12(evo)-7(l)0(u)-7(tio)-7(nar)-17(y)17( a)-15(n)5(al)-12(ysi)-12(s)2(: )-12(w)10(e)-3( d)-7(o)-7( no)-7(t allo)-7(w)10( )-12(f)7(o)-7(r no)-7(ise i)-12(n)5( co)-19(m)18(p)-19(uti)-12(ng relati)-12(ve b)-7(e)-3(st)]TJ T* 0.005 Tc -0.002 Tw [(res)8(pon)11(s)8(e)3(s)8(,)2( in)11( s)8(a)-9(m)24(p)-1(li)6(ng)11( s)8(t)6(rat)6(e)-9(g)11(i)6(es)8( )-12(f)13(r)1(o)-13(m)24( th)11(e popu)11(l)6(a)3(t)6(i)6(o)-1(n)11( or i)6(n)11( pa)-9(y)23(o)-13(ff)13(s)8(.)]TJ ET endstream endobj 131 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F3 38 0 R /F4 43 0 R /F5 46 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F14 128 0 R /F15 132 0 R /T47 133 0 R /T48 134 0 R /T49 135 0 R /T50 136 0 R /T51 137 0 R /T52 138 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 139 0 obj << /Length 8487 >> stream BT /F3 1 Tf 12 0 0 12 300.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc (14)Tj -17.5 -3 TD -0.001 Tc 0.171 Tw [(transfer )-10(a)-7(g)9(ainst a r)-8(e)3(d fla)-7(g)9(, )-10(and a r)-8(e)3(d fla)-7(g)9( to low trans)-12(f)2(er )-10(a)-7(g)9(ainst )-10(g)9(r)2(e)-7(e)3(n fla)-7(g)9( )-10(and hig)9(h)]TJ 0 -1.66 TD -0.002 Tc 0.092 Tw [(t)-4(r)1(ansfer a)-8(g)8(ai)-4(nst)-4( )10(a )10(r)-9(e)2(d )10(fl)-4(a)-8(g)8(. )10(Th)-12(e )10(st)-4(rat)-4(e)-8(g)-12(y)18( )10(i)-4(t)-4(s)-3(el)-4(f )10(i)-4(s)-3( )10(t)-4(o)-2( gi)-4(ve hi)-14(g)8(h)-2( t)-4(r)1(ansf)-9(er on )-10(g)8(r)-9(een )-10(fl)-4(a)-8(g)8(, l)-4(o)-2(w)]TJ 0 -1.67 TD 0.042 Tw [(t)-4(r)1(ansfer on )-10(red fl)-14(a)-8(g)8(. That)-4( i)-4(s)-3( a )-10(g)8(r)-9(een fl)-14(a)-8(g)8( m)-4(eans t)-4(h)-2(e pl)-4(a)-18(y)18(e)-8(r)1( i)-4(s)-3( a )-10(m)-4(e)2(m)-4(b)-12(er )-10(of )-10(t)-4(h)-2(e )-10(t)-4(e)-8(am)-4(;)-4( )-10(t)-4(eam)]TJ T* -0.001 Tc 0.061 Tw [(members )10(ar)-8(e )10(supposed )10(to g)9(i)-3(ve )10(hi)-13(g)9(h)-1( )10(transf)-8(ers to team memb)-11(ers and low tr)-8(ansfe)-7(r)2(s to non-)]TJ 0 -1.66 TD 0.001 Tc 0.089 Tw [(te)5(a)5(m)-1( )10(me)5(mbe)5(r)4(s. B)8(e)5(ha)5(vin)-9(g)11( a)5(s)0( )10(a)5( )10(te)5(a)5(m)-1( )10(me)5(mb)-9(e)5(r)4( is the)5( tic)5(ke)5(t fo)-9(r a)5(d)1(mission to the)5( te)5(a)5(m; the)]TJ 0 -1.67 TD 0.129 Tw [(pe)5(na)5(lt)-11(y)21( for )10(fa)5(iling)11( )10(to )10(be)5(have)5( a)5(s)0( )-10(a)5( te)5(a)5(m)-1( me)5(mber is e)5(x)-9(pulsion from the)5( te)5(a)5(m)-1(. The)5( othe)5(r)]TJ T* 0.099 Tw [(stra)5(teg)-9(y)21( in this c)5(l)-1(a)5(ss is )]TJ /F8 1 Tf 9.75 0 TD -0.001 Tc (red-team)Tj /F3 1 Tf 3.6 0 TD 0 Tc 0.11 Tw [( which us)-11(es the same info)-10(rmation s)-11(y)20(stem, but uses the)]TJ -13.35 -1.66 TD -0.001 Tc 0.001 Tw [(convention of hig)9(h)-1( t)-13(r)2(ansfe)-7(r)2( on r)-8(e)3(d and low trans)-12(f)2(er on )-10(green.)]TJ /F11 1 Tf 0 -2.17 TD 0.011 Tw [(Theore)-7(m)12( 5.1:)]TJ /F8 1 Tf 5.72 0 TD [( If )]TJ /F9 1 Tf 3.37 0 TD 0 Tc 0 Tw (\022)Tj /F7 1 Tf -2.01 0 TD (C)Tj /F6 1 Tf 0.95 0 TD (\035)Tj /F8 1 Tf 1.83 0 TD 0.01 Tw [( and )]TJ /F7 1 Tf 2.25 0 TD 0 Tw (I)Tj /F8 1 Tf 0.78 0 TD 0.001 Tc 0.019 Tw [( suffic)5(ie)5(ntly)5( small the)5( unique)5( stoc)5(hastic)5(ally)5( stable)5( state)5( is)]TJ -12.89 -1.67 TD 0.069 Tw [(alway)5(s)0( se)5(lfish; if )]TJ /F9 1 Tf 9.41 0 TD 0 Tc 0 Tw (\022)Tj /F7 1 Tf -2.01 0 TD (C)Tj /F6 1 Tf 0.94 0 TD (\037)Tj /F16 1 Tf 1.84 0 TD 0.07 Tw [( the unique stochastically stable state )-10(places )-10(weight )-10(\275 )-10(on )-10(each)]TJ -10.18 -1.66 TD -0.001 Tc 0.001 Tw [(green-team and r)-12(e)3(d-team.)]TJ 0 -2.17 TD (Proof: )Tj /F3 1 Tf 2.86 0 TD [(See Appendix)-11( A.)]TJ /F12 1 Tf 30.14 -1.67 TD 0 Tc 0 Tw (\346)Tj /F3 1 Tf -33 -1.66 TD 0.001 Tc 0.089 Tw [(Notic)5(e)5( tha)5(t)-1( this is ve)5(ry)21( sharp: for )]TJ /F9 1 Tf 16.27 0 TD 0 Tc 0 Tw (\022)Tj /F7 1 Tf -2.01 0 TD (C)Tj /F6 1 Tf 0.95 0 TD (\035)Tj /F3 1 Tf 1.83 0 TD 0.1 Tw [( )10(we)4( )-10(g)10(e)4(t )-10(a)4(l)-2(wa)-16(y)20(s)-1( se)4(lfish; for )]TJ /F9 1 Tf 13.54 0 TD 0 Tw (\022)Tj /F7 1 Tf -2.01 0 TD (C)Tj /F6 1 Tf 0.94 0 TD (\037)Tj /F3 1 Tf 1.84 0 TD 0.1 Tw [( we)4( )-10(g)10(e)4(t the)]TJ -31.35 -1.67 TD 0.15 Tw [(two team strate)-6(g)10(i)-2(es as the)-6( stochasticall)-22(y)20( stable set. This c)-6(a)4(n be )-20(compared )-10(to )-10(J)-11(ohnson,)]TJ T* -0.001 Tc 0.061 Tw [(L)10(e)3(vin)-11(e)3( )10(and Pesendo)-11(rfe)-7(r [)-8(1999])-8( who ex)-11(amine the standard model under slig)9(htl)-23(y)19( diff)-8(ere)-7(n)-1(t)]TJ 0 -1.66 TD -0.002 Tc 0.072 Tw [(assum)-4(p)-2(t)-4(i)-4(ons )10(and )10(wi)-4(t)-4(h)-2( )10(el)-4(aborat)-4(e cal)-4(cul)-4(a)2(t)-4(i)-4(ons ar)-9(e abl)-4(e)2( t)-4(o)-2( )-10(get)-4( t)-4(h)-2(e t)-4(eam)-4( st)-4(rat)-14(e)-8(g)8(i)-4(es em)-4(er)-9(g)8(i)-4(n)-12(g)]TJ 0 -1.67 TD -0.001 Tc 0.001 Tw [(as stochasticall)-23(y)19( stable onl)-23(y)19( for )]TJ /F9 1 Tf 15.07 0 TD 0 Tc 0 Tw (\024)Tj /F7 1 Tf -2.05 0 TD (C)Tj /F6 1 Tf 0.94 0 TD (\037)Tj /F3 1 Tf 1.84 0 TD (.)Tj /F1 1 Tf 14.04 0 0 14.04 90.09 320.01 Tm 0.004 Tw [(6. Characte)9(rizat)8(i)-4(on of S)17(t)0(ochast)8(ica)9(l)-4(l)-13(y)35( S)17(t)25(able S)17(t)25(a)9(tes)]TJ /F3 1 Tf 12 0 0 12 126.09 297.09 Tm -0.001 Tc 0.121 Tw [(W)-7(e)3( first describe )]TJ /F6 1 Tf 7.63 0 TD 0 Tc 0 Tw (8)Tj /F3 1 Tf 0.97 0 TD 0.001 Tc 0.119 Tw [( in g)11(r)-6(e)5(a)5(t)-1(e)5(r)4( d)-9(e)5(ta)5(il a)5(s)0( a)5( )-10(p)-9(r)4(e)5(limina)5(r)-16(y)21( )-10(to )-10(de)5(finin)-9(g)11( )-10(the)5( )-10(modifie)5(d)]TJ -11.6 -1.67 TD -0.002 Tc 0.142 Tw [(resi)-4(st)-4(ance, )10(whi)-14(c)2(h )10(can b)-12(e)2( used t)-4(o)-2( )-10(g)8(i)-4(ve )-10(an ex)-12(act)-4( cha)-8(r)1(act)-14(eri)-4(z)-8(at)-4(i)-4(on of st)-4(ochast)-4(i)-4(cal)-4(l)-24(y)18( st)-4(abl)-4(e)]TJ T* [(st)-4(at)-4(e.)]TJ 3 -1.66 TD 0.012 Tw [(Denote b)-22(y)18( )]TJ /T53 1 Tf 8.391 0 0 8.391 189.45 233.01 Tm 0 Tc 0 Tw (K)Tj /F6 1 Tf 12.024 0 0 12.024 181.29 237.09 Tm (8)Tj /F3 1 Tf 12 0 0 12 197.01 237.09 Tm -0.001 Tc 0.011 Tw [( the subset of )]TJ /F7 1 Tf 11.97 0 0 11.97 266.73 237.09 Tm 0 Tc 0 Tw (X)Tj /F6 1 Tf 0.9825 0 TD 0.28 Tc (\2118)Tj /F3 1 Tf 12 0 0 12 301.05 237.09 Tm -0.001 Tc 0.011 Tw [( for which )]TJ ET q 1 i 356.13 249.09 54.84 -18 re W* n BT /F9 1 Tf 12 0 0 12 356.13 237.09 Tm 0.71 Tc [(\003\010)80(\011)]TJ ET Q q 1 i 367.17 249.09 49.68 -18 re W* n BT /F5 1 Tf 12 0 0 12 367.17 237.09 Tm 2.78 Tc (3K)Tj ET Q BT /F7 1 Tf 12 0 0 12 379.17 237.09 Tm 0 Tc 0 Tw (X)Tj /F6 1 Tf 1.3 0 TD (b)Tj /F4 1 Tf 1.84 0 TD -0.002 Tc 0.022 Tw [(. Most)-4( of t)-4(h)-2(e \223act)-4(i)-4(o)-2(n)-12(\224)]TJ -27.23 -1.67 TD 0.192 Tw [(t)-4(a)2(kes pl)-4(ace i)-4(n)-2( )]TJ /T54 1 Tf 8.355 0 0 8.355 175.89 213.09 Tm 0 Tc 0 Tw (\022)Tj /F6 1 Tf 11.975 0 0 11.975 167.61 217.05 Tm (8)Tj /F4 1 Tf 12 0 0 12 183.33 217.05 Tm 0.2 Tw [( in the)4( se)4(nse)4( tha)4(t)-2( it is unlike)4(l)-12(y)20( tha)4(t)-2( the)4(r)-7(e)4( a)4(r)-7(e)4( more)4( tha)4(n)0( two pu)-10(re)]TJ -7.77 -1.67 TD 0.18 Tw [(strateg)10(i)-2(es bein)-10(g)10( used in the population at )-10(an)-20(y)20( )-10(moment )-10(o)-10(f)3( )-10(time. )-10(The )-10(space )]TJ /T54 1 Tf 8.355 0 0 8.355 482.85 193.05 Tm 0 Tw (\022)Tj /F6 1 Tf 11.975 0 0 11.975 474.57 197.01 Tm (8)Tj /F4 1 Tf 12 0 0 12 490.29 197.01 Tm -0.001 Tc 0.191 Tw [( has a)]TJ -33.35 -1.66 TD 0.201 Tw [(relativel)-23(y)19( )10(simple topolog)9(ical stru)-11(cture, )-10(consisting)9( of pur)-8(e strate)-7(g)9(i)-3(es )-10(and the se)-7(g)9(m)-3(ents)]TJ 0 -1.67 TD 0 Tc 0 Tw [(connectin)-10(g)10( them. This has important consequ)-10(e)4(nc)-6(es:)]TJ /F11 1 Tf 0 -2.17 TD -0.001 Tc 0.231 Tw [(Lemma 6.2:)]TJ /F8 1 Tf 5.33 0 TD [( If )]TJ /T54 1 Tf 8.355 0 0 8.355 207.21 127.05 Tm 0 Tc 0 Tw (\022)Tj /F7 1 Tf 11.975 0 0 11.975 175.65 131.01 Tm (X)Tj /F6 1 Tf 0.9821 0 TD 0.29 Tc (\2118)Tj /F8 1 Tf 12 0 0 12 214.05 131.01 Tm 0 Tc (, )Tj /F9 1 Tf 1.48 0 TD 0.86 Tc (\014\002)Tj /F7 1 Tf -0.55 0 TD 0.369 Tc [(TT)-1470(X)]TJ /F6 1 Tf 2.36 0 TD 0 Tc (\211)Tj /F8 1 Tf 1.94 0 TD (, )Tj /F9 1 Tf 1.54 0 TD 0.72 Tc [(\010\007)720(\011)-1270(\010)160(\011)]TJ /F5 1 Tf -0.63 0 TD 3.11 Tc (33)Tj /F7 1 Tf 0.99 0 TD 3.099 Tc (TT)Tj ET q 1 i 318.93 143.01 24 -18 re W* n BT /F6 1 Tf 12 0 0 12 318.93 131.01 Tm 0 Tc (\036)Tj ET Q BT /F8 1 Tf 12 0 0 12 357.69 131.01 Tm 0.002 Tc 0.238 Tw [( with )]TJ ET q 1 i 399.33 143.01 122.76 -18 re W* n BT /F9 1 Tf 12 0 0 12 399.33 131.01 Tm 0.37 Tc [(\010\011)-1540(\010)-160(\007)360(\011)-1530(\010)-170(\002)380(\011)-990(\020)]TJ ET Q q 1 i 403.05 143.01 101.64 -18 re W* n BT /F5 1 Tf 12 0 0 12 403.05 131.01 Tm 2.649 Tc [(SS)-350(S)]TJ ET Q q 1 i 392.49 143.01 101.64 -18 re W* n BT /F7 1 Tf 12 0 0 12 392.49 131.01 Tm 2.499 Tc [(TT)-330(T)]TJ ET Q q 1 i 416.13 143.01 105.96 -18 re W* n BT /F6 1 Tf 12 0 0 12 416.13 131.01 Tm 2.636 Tc [(\037\037)-150(\037)]TJ ET Q BT 12 0 0 12 90.09 111.09 Tm 0.001 Tc [(the)5(n)1( )]TJ /F9 1 Tf 11.97 0 0 11.97 125.13 111.09 Tm 0 Tc 0 Tw (\002)Tj /F7 1 Tf -0.7519 0 TD 1.845 Tc (TX)Tj /F6 1 Tf 1.4336 0 TD 0 Tc (\211)Tj /F8 1 Tf 12 0 0 12 155.73 111.09 Tm (.)Tj ET endstream endobj 140 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F1 36 0 R /F3 38 0 R /F4 43 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F11 62 0 R /F12 90 0 R /F16 141 0 R /T53 142 0 R /T54 143 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 145 0 obj << /Length 15832 >> stream BT /F3 1 Tf 12 0 0 12 300.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc (15)Tj /F8 1 Tf -17.5 -3 TD -0.001 Tc (Proof: )Tj /F3 1 Tf 2.89 0 TD -0.013 Tc [(If)-10( )]TJ /F9 1 Tf 1.68 0 TD 0.86 Tc (\014\002)Tj /F7 1 Tf -0.55 0 TD 0.369 Tc [(TT)-1470(X)]TJ /F6 1 Tf 2.36 0 TD 0 Tc 0 Tw (\211)Tj /F3 1 Tf 1.94 0 TD -0.001 Tc 0.021 Tw [( there must be a r)-8(e)3(lative best respons)-12(e path, or )-10(equivalentl)-23(y)19( a path of)]TJ -8.32 -1.66 TD 0.121 Tw [(z)-7(e)3(ro resistance b)-11(e)3(twe)-7(e)3(n the two. Such a p)-11(a)3(th cannot pass throu)-11(g)9(h )]TJ /T55 1 Tf 8.355 0 0 8.355 432.81 680.13 Tm 0 Tc 0 Tw (\021)Tj /F6 1 Tf 11.975 0 0 11.975 424.77 684.09 Tm (8)Tj /F3 1 Tf 12 0 0 12 439.53 684.09 Tm 0.001 Tc 0.129 Tw [(, so it must)9( pass)]TJ -29.12 -1.67 TD 0 Tc [(throug)10(h )]TJ /F9 1 Tf 4.32 0 TD 0 Tw (\007)Tj /F7 1 Tf -0.76 0 TD (T)Tj /F3 1 Tf 1.22 0 TD 0.001 Tc -0.001 Tw [(. This me)5(a)5(n)1(s tha)5(t)-1( )]TJ /F9 1 Tf 11.97 0 0 11.97 243.81 664.05 Tm 0 Tc 0 Tw (\007)Tj /F7 1 Tf -0.7519 0 TD 1.675 Tc (TX)Tj /F6 1 Tf 1.2532 0 TD 0 Tc (\211)Tj /F3 1 Tf 12 0 0 12 272.37 664.05 Tm [( a)4(s)-1( we)4(ll.)]TJ /F12 1 Tf 19.92 -1.67 TD (\346)Tj /F3 1 Tf -32.11 -1.66 TD 0.002 Tc 0.058 Tw [(We)6( illustra)6(te)6( )]TJ /F6 1 Tf 11.975 0 0 11.975 194.61 624.09 Tm 0 Tc 0 Tw (8)Tj /F3 1 Tf 12 0 0 12 210.21 624.09 Tm 0.06 Tw [( in the)4( fig)10(u)0(re)4( b)-10(e)4(low. Here)4( there)4( are)4( 4 )-10(points )]TJ /F9 1 Tf 12.024 0 0 12.024 431.97 624.09 Tm 1.127 Tc [([)190(\014\014\014)-50(])]TJ /T56 1 Tf 8.391 0 0 8.391 442.65 628.89 Tm 1.234 Tc [(!")28(#)-158($)]TJ /F5 1 Tf 12.024 0 0 12.024 437.01 624.09 Tm 0.976 Tc [(SS)-20(S)-10(S)]TJ /F3 1 Tf 12 0 0 12 508.89 624.09 Tm 0.002 Tc 0.068 Tw [( in)]TJ /T57 1 Tf 8.355 0 0 8.355 100.77 600.21 Tm 0 Tc 0 Tw (\021)Tj /F5 1 Tf 11.975 0 0 11.975 123.09 604.05 Tm (3)Tj /F6 1 Tf -2.5554 0 TD 0.743 Tc (8\036)Tj /F3 1 Tf 12 0 0 12 134.13 604.05 Tm -0.001 Tc 0.071 Tw [(. )10(The dashes c)-7(onnectin)-11(g)9( those pur)-8(e strate)-7(g)9(i)-3(es )-10(repr)-8(esent points on the )-10(g)9(r)2(id )]TJ /T58 1 Tf 8.355 0 0 8.355 508.17 608.85 Tm 0 Tc 0 Tw (M)Tj /F6 1 Tf 11.975 0 0 11.975 500.01 604.05 Tm (4)Tj /F3 1 Tf 12 0 0 12 518.73 604.05 Tm (;)Tj -35.72 -1.67 TD 0.001 Tc 0.079 Tw [(tha)5(t)-1( is, they)21( are)5( mix)-9(ture)5(s be)5(twe)5(e)5(n)1( e)5(x)-9(a)5(c)5(t)-1(l)-21(y)21( two pure)5( )-10(stra)5(teg)11(i)-1(e)5(s)0(. )-20(\(Note)5( )-10(tha)5(t)-1( )-10(the)5( )-10(dra)5(w)3(in)-9(g)11( )-10(is)]TJ 0 -1.66 TD -0.001 Tc 0.061 Tw [(not )10(ex)-11(act, )10(since there should be the s)-12(a)3(me number of)-8( points )]TJ /F9 1 Tf 11.931 0 0 11.931 408.45 564.09 Tm 0 Tc 0 Tw (\021)Tj /F5 1 Tf -2.0819 0 TD (M)Tj /F6 1 Tf 1.1265 0 TD (\016)Tj /F3 1 Tf 12 0 0 12 416.73 564.09 Tm -0.002 Tc 0.062 Tw [( bet)-4(w)0(een )-10(ea)-8(ch pai)-4(r)1( of)]TJ -27.22 -1.67 TD 0.122 Tw [(pure st)-4(rat)-4(e)-8(g)8(i)-4(es.)-12(\))1( Ther)-9(e a)-8(r)1(e t)-4(h)-2(re)-8(e poi)-4(nt)-4(s )]TJ /F9 1 Tf 16.53 0 TD 1.05 Tc [([\014)-150(\014)-160(])]TJ /T59 1 Tf 8.379 0 0 8.379 302.01 548.85 Tm 1.67 Tc [(XY)29(Z)]TJ /F7 1 Tf 12 0 0 12 294.21 544.05 Tm 0.89 Tc [(XX)40(X)]TJ /F3 1 Tf 4.77 0 TD 0.001 Tc 0.129 Tw [( in )]TJ /T57 1 Tf 8.355 0 0 8.355 381.09 540.21 Tm 2.581 Tc (\022\021)Tj /F9 1 Tf 11.975 0 0 11.975 389.37 544.05 Tm 0 Tc 0 Tw (<)Tj /F6 1 Tf -1.423 0 TD 1.475 Tc (88)Tj /F3 1 Tf 12 0 0 12 413.97 544.05 Tm -0.001 Tc 0.131 Tw [(. Each one is a set of)]TJ -26.99 -1.67 TD 0.001 Tc 0.049 Tw (points in )Tj /T57 1 Tf 8.355 0 0 8.355 146.73 520.17 Tm 0 Tc 0 Tw (\022)Tj /T58 1 Tf -0.0431 1.0341 TD (M)Tj /F6 1 Tf 11.975 0 0 11.975 138.21 524.01 Tm (4)Tj /F3 1 Tf 12 0 0 12 156.93 524.01 Tm 0.05 Tw (. The point )Tj /T60 1 Tf 8.379 0 0 8.379 224.49 528.81 Tm 0 Tw (Z)Tj /F7 1 Tf 12 0 0 12 216.69 524.01 Tm (X)Tj /F3 1 Tf 1.28 0 TD -0.001 Tc 0.051 Tw [( has )]TJ /F9 1 Tf 12.024 0 0 12.024 264.81 524.01 Tm 1.077 Tc [(\010\011)-299([)120(\014)-110(])]TJ /T61 1 Tf 8.391 0 0 8.391 277.29 528.81 Tm 3.999 Tc [(Z")2678($)]TJ /F5 1 Tf 12.024 0 0 12.024 257.37 524.01 Tm 3.712 Tc [(3S)2716(S)]TJ /F7 1 Tf 1.008 0 TD 0 Tc 0 Tw (X)Tj /F6 1 Tf 1.7565 0 TD (\036)Tj /F3 1 Tf 12 0 0 12 347.37 524.01 Tm 0.06 Tw [(, )10(and )10(consists of two points in )]TJ /T57 1 Tf 8.355 0 0 8.355 508.89 520.17 Tm 0 Tw (\022)Tj /T58 1 Tf -0.0431 1.0341 TD (M)Tj /F6 1 Tf 11.975 0 0 11.975 500.37 524.01 Tm (4)Tj /F3 1 Tf 12 0 0 12 519.09 524.01 Tm (.)Tj -35.75 -1.66 TD 0.22 Tw (The points )Tj /F9 1 Tf 6.23 0 TD 0 Tw (\014)Tj /T60 1 Tf 8.379 0 0 8.379 159.81 508.89 Tm 1.67 Tc (XY)Tj /F7 1 Tf 12 0 0 12 152.01 504.09 Tm 0.89 Tc (XX)Tj /F3 1 Tf 2.78 0 TD -0.003 Tc 0.223 Tw [( each )-10(h)-13(a)1(ve )]TJ /F9 1 Tf 12.024 0 0 12.024 256.65 504.09 Tm 1.067 Tc [(\010\014)-180(\011)-309([)140(\014)-120(])]TJ /T62 1 Tf 8.391 0 0 8.391 269.13 508.89 Tm 1.667 Tc [(XY)-2302(!)433($)]TJ /F5 1 Tf 12.024 0 0 12.024 249.21 504.09 Tm 5.228 Tc [(3S)4262(S)]TJ /F7 1 Tf 1.008 0 TD 0.887 Tc (XX)Tj /F6 1 Tf 3.2735 0 TD 0 Tc 0 Tw (\036)Tj /F3 1 Tf 12 0 0 12 357.21 504.09 Tm 0.23 Tw (. The point )Tj /T60 1 Tf 8.379 0 0 8.379 431.25 508.89 Tm 0 Tw (X)Tj /F7 1 Tf 12 0 0 12 423.45 504.09 Tm (X)Tj /F3 1 Tf 1.28 0 TD 0.23 Tw [( c)4(onsists of two)]TJ -29.06 -1.67 TD 0.001 Tc -0.001 Tw (points in )Tj /T57 1 Tf 8.355 0 0 8.355 145.53 480.21 Tm 0 Tc 0 Tw (\022)Tj /T58 1 Tf -0.0431 1.0341 TD (M)Tj /F6 1 Tf 11.975 0 0 11.975 137.01 484.05 Tm (4)Tj /F3 1 Tf 12 0 0 12 155.73 484.05 Tm (; the point )Tj /T60 1 Tf 8.379 0 0 8.379 217.65 488.85 Tm (Y)Tj /F7 1 Tf 12 0 0 12 210.09 484.05 Tm (X)Tj /F3 1 Tf 1.28 0 TD [( a sing)10(leton in )]TJ /T57 1 Tf 8.355 0 0 8.355 306.93 480.21 Tm (\022)Tj /T58 1 Tf -0.0431 1.0341 TD (M)Tj /F6 1 Tf 11.975 0 0 11.975 298.41 484.05 Tm (4)Tj /F3 1 Tf 12 0 0 12 317.13 484.05 Tm (.)Tj -15.92 -1.67 TD -0.003 Tc 0.033 Tw [(The cas)-14(e of )]TJ /T60 1 Tf 8.379 0 0 8.379 195.93 468.81 Tm 0 Tc 0 Tw (X)Tj /F7 1 Tf 12 0 0 12 188.13 464.01 Tm (X)Tj /F3 1 Tf 1.28 0 TD -0.001 Tc 0.031 Tw [( and )]TJ /T60 1 Tf 8.379 0 0 8.379 237.93 468.81 Tm 0 Tc 0 Tw (Z)Tj /F7 1 Tf 12 0 0 12 230.13 464.01 Tm (X)Tj /F3 1 Tf 1.28 0 TD -0.001 Tc 0.041 Tw [( )10(are )10(in a sense t)-23(y)19(pic)-7(a)3(l of points in )]TJ /T57 1 Tf 8.355 0 0 8.355 424.29 460.17 Tm 2.581 Tc (\022\021)Tj /F9 1 Tf 11.975 0 0 11.975 432.57 464.01 Tm 0 Tc 0 Tw (<)Tj /F6 1 Tf -1.423 0 TD 1.475 Tc (88)Tj /F3 1 Tf 12 0 0 12 457.17 464.01 Tm 0.001 Tc 0.039 Tw [( in c)5(onsisting)]TJ -30.59 -1.66 TD 0 Tc 0.02 Tw [(of two points in )]TJ /T57 1 Tf 8.355 0 0 8.355 180.57 440.25 Tm 0 Tw (\022)Tj /T58 1 Tf -0.0431 1.034 TD (M)Tj /F6 1 Tf 11.975 0 0 11.975 172.05 444.09 Tm (4)Tj /F3 1 Tf 12 0 0 12 190.77 444.09 Tm 0.02 Tw [(. Two se)4(e)4( this, le)4(t us re)4(fer to )-10(a)4( )-10(mix)-10(e)4(d)0( )-10(stra)4(te)4(g)-10(y)20( )-20(e)4(quilibrium )-10(in )-10(a)4( )-10(ga)4(me)]TJ -8.39 -1.67 TD 0.18 Tw [(using)10( )10(a )10(subset consisting)10( )10(of )10(two )10(pur)-7(e strate)-6(g)10(i)-12(es only)20( )-10(a)-6(s)-1( a )]TJ /F8 1 Tf 24.77 0 TD 0.001 Tc 0.189 Tw [(re)5(lativ)5(e)5( mix)5(e)5(d)1( e)5(quilibrium)]TJ /F3 1 Tf 10.98 0 TD 0 Tc 0 Tw (.)Tj -35.75 -1.67 TD -0.002 Tc 0.022 Tw [(R)-5(ecal)-4(l)-4( t)-4(h)-2(at)-4( an)-22(y)18( poi)-4(nt)-4( i)-4(n)-2( )]TJ /F6 1 Tf 9.89 0 TD 0 Tc 0 Tw (8)Tj /F3 1 Tf 0.96 0 TD 0.03 Tw [( consists of points in )]TJ /T57 1 Tf 8.355 0 0 8.355 334.65 400.17 Tm 0 Tw (\022)Tj /T58 1 Tf -0.0431 1.0341 TD (M)Tj ET q 1 i 326.13 416.01 18.72 -18.12 re W* n BT /F6 1 Tf 11.975 0 0 11.975 326.13 404.01 Tm (4)Tj ET Q BT /F3 1 Tf 12 0 0 12 344.85 404.01 Tm -0.001 Tc 0.031 Tw [( that are minimal invariant under the)]TJ -21.23 -1.66 TD 0.561 Tw [(relative best-)-8(r)2(esponse d)-21(y)19(n)-11(a)3(mic. Consider )]TJ ET q 1 i 351.09 398.01 43.92 -19.92 re W* n BT /F9 1 Tf 12.024 0 0 12.024 351.09 384.09 Tm 0.947 Tc [([\014)-260(])]TJ ET Q q 1 i 328.41 398.13 52.2 -13.56 re W* n BT /T63 1 Tf 8.391 0 0 8.391 328.41 388.89 Tm 3.813 Tc (ZZ)Tj ET Q BT /F7 1 Tf 12.024 0 0 12.024 320.61 384.09 Tm 2.364 Tc [(XT)1538(T)]TJ /T64 1 Tf 8.391 0 0 8.391 380.73 388.89 Tm 0 Tc 0 Tw (;)Tj /F6 1 Tf 12.024 0 0 12.024 338.01 384.09 Tm (\036)Tj /F3 1 Tf 12 0 0 12 395.01 384.09 Tm 0.001 Tc 0.569 Tw [(. )10(Ruling)11( )10(out tie)5(s, a)5(n)1(d)]TJ -25.41 -1.67 TD 0.049 Tw [(re)5(me)5(mbe)5(r)4(in)-9(g)11( tha)5(t)-1( onl)-21(y)21( one)5( pla)-15(y)21(er move)5(s )-10(a)5(t)-1( a)5( time)5(, this me)5(a)5(n)1(s tha)5(t)-1( )]TJ /T65 1 Tf 8.391 0 0 8.391 429.33 368.85 Tm 0 Tc 0 Tw (:)Tj /F7 1 Tf 12.028 0 0 12.028 422.13 364.05 Tm (T)Tj /F3 1 Tf 12 0 0 12 438.69 364.05 Tm 0.001 Tc 0.059 Tw [( is a)5( re)5(la)5(tive)5( be)5(st)]TJ -29.05 -1.67 TD -0.001 Tc 0.191 Tw (response to )Tj /T66 1 Tf 8.379 0 0 8.379 161.73 348.81 Tm 0 Tc 0 Tw (Z)Tj /F7 1 Tf 12 0 0 12 154.41 344.01 Tm (T)Tj /F3 1 Tf 1.22 0 TD -0.001 Tc 0.191 Tw [( and vice versa)-7(.)-1( Consequentl)-23(y)19(, )]TJ /T66 1 Tf 8.379 0 0 8.379 340.53 348.81 Tm 0 Tc 0 Tw (Z)Tj /F7 1 Tf 12 0 0 12 332.73 344.01 Tm (X)Tj /F3 1 Tf 1.28 0 TD -0.002 Tc 0.192 Tw [( i)-4(s)-3( a t)-4(w)0(o-cy)8(c)-8(l)-4(e. B)-5(e)-8(cause )-10(onl)-24(y)18( )-10(one)]TJ -21.5 -1.66 TD 0 Tc 0.01 Tw [(play)20(er )10(moves )10(at a )10(time, there )-10(cannot be )-10(c)-16(y)20(cles of len)-10(g)10(th lon)-10(g)10(er than 2 in )]TJ /T57 1 Tf 8.355 0 0 8.355 451.17 320.25 Tm 2.581 Tc (\022\021)Tj /F9 1 Tf 11.975 0 0 11.975 459.45 324.09 Tm 0 Tc 0 Tw (<)Tj /F6 1 Tf -1.423 0 TD 1.475 Tc (88)Tj /F3 1 Tf 12 0 0 12 484.05 324.09 Tm 0.001 Tc 0.009 Tw [(. Notic)5(e)]TJ -32.83 -1.67 TD -0.002 Tc 0.172 Tw [(t)-4(h)-2(at)-4( )10(such a t)-4(w)0(o-c)-18(y)18(c)-8(l)-4(e a)-8(r)1(i)-4(s)-3(es when )]TJ /F9 1 Tf 12.024 0 0 12.024 280.41 304.05 Tm 0 Tc 0 Tw (\014)Tj /T67 1 Tf 8.391 0 0 8.391 275.85 308.85 Tm 1.568 Tc (Z:)Tj /F7 1 Tf 12.024 0 0 12.024 268.53 304.05 Tm 0.826 Tc (TT)Tj /F3 1 Tf 12 0 0 12 302.13 304.05 Tm -0.001 Tc 0.171 Tw [( are s)-12(e)3(par)-8(a)3(ted b)-21(y)19( a non)-11(-g)9(r)-8(i)-3(d point that is a)]TJ -17.67 -1.67 TD 0 Tc 0.06 Tw [(relative )10(mix)-10(ed )10(strateg)-10(y)20( equilibrium stable in the continuous time best response d)-20(y)20(namic.)]TJ 0 -1.66 TD 0.15 Tw [(Of )10(c)4(ours)-11(e)4( )10(if suc)4(h)0( a)4( )-10(re)4(la)4(tive)4( mix)-10(e)4(d)0( e)4(quilibrium wa)4(s a)4(c)4(t)-2(ua)4(ll)-22(y)20( on a)4( )-10(grid point, the)4(n)0( tha)4(t)]TJ 0 -1.67 TD 0.05 Tw [(point would as a sing)10(leton )-10(set )-10(be )-10(in )]TJ /T57 1 Tf 8.355 0 0 8.355 278.49 240.21 Tm 2.581 Tc (\022\021)Tj /F9 1 Tf 11.975 0 0 11.975 286.77 244.05 Tm 0 Tc 0 Tw (<)Tj /F6 1 Tf -1.423 0 TD 1.475 Tc (88)Tj /F3 1 Tf 12 0 0 12 311.37 244.05 Tm -0.001 Tc 0.061 Tw [( such as )]TJ /F7 1 Tf 3.82 0 TD 0 Tc 0 Tw (X)Tj /F3 1 Tf 1.28 0 TD 0.06 Tw [(. Howe)4(ve)4(r, it is unlike)4(l)-12(y)20( th)-10(a)4(t)-2( a)]TJ -23.54 -1.67 TD 0.001 Tc 0.379 Tw [(re)5(la)5(tive)5( )10(mix)-9(e)5(d)1( )10(e)5(quilibrium )10(will )10(a)5(c)5(t)-1(ua)5(ll)-11(y)21( lie)5( on a)5( )-10(g)11(r)4(id point. )-10(I)14(f)4( )-10(a)5( re)5(la)5(tive)5( mix)-9(e)5(d)]TJ 0 -1.66 TD 0 Tc 0.07 Tw [(equilibrium )10(is unstable in the continuous time best response d)-10(y)20(n)-10(a)4(mic, then ther)-7(e will be)]TJ 0 -1.67 TD 0 Tw [(no correspondin)-10(g)10( point in )]TJ /T57 1 Tf 8.355 0 0 8.355 227.85 180.21 Tm (\022)Tj /F6 1 Tf 11.975 0 0 11.975 219.21 184.05 Tm (8)Tj /F3 1 Tf 12 0 0 12 234.81 184.05 Tm (.)Tj -9.06 -1.67 TD 0.08 Tw (Suppose that )Tj /T68 1 Tf 8.355 0 0 8.355 238.89 160.05 Tm 0 Tw (\022)Tj /F9 1 Tf 11.975 0 0 11.975 202.41 164.01 Tm (\014)Tj /F7 1 Tf -0.5912 0 TD 0.382 Tc (XX)Tj /F6 1 Tf 1.9942 0 TD 0.28 Tc (\2118)Tj /F10 1 Tf -0.8618 0.02 TD 0 Tc (%)Tj /F3 1 Tf 12 0 0 12 245.73 164.01 Tm -0.002 Tc 0.082 Tw [(. W)-8(e)2( sa)-8(y)18( t)-4(h)-2(at)-4( t)-4(h)-2(e)-18(y)18( )-10(are )]TJ /F8 1 Tf 9.38 0 TD 0 Tc [(adjac)-6(ent)]TJ /F3 1 Tf 3.45 0 TD 0.09 Tw [( if it possible)4( to g)10(o)0( from)]TJ -25.8 -1.66 TD 0.39 Tw [(one to the other without passing)10( th)-10(rou)-10(g)10(h )-10(another )-10(point )-10(in )]TJ /T68 1 Tf 8.355 0 0 8.355 423.93 140.13 Tm 0 Tw (\022)Tj /F6 1 Tf 11.975 0 0 11.975 415.65 144.09 Tm (8)Tj /F3 1 Tf 12 0 0 12 431.37 144.09 Tm -0.001 Tc 0.401 Tw [(. More pre)-7(c)3(isel)-13(y)19(,)]TJ /T68 1 Tf 8.355 0 0 8.355 136.29 120.09 Tm 0 Tc 0 Tw (\022)Tj /F9 1 Tf 11.975 0 0 11.975 99.81 124.05 Tm (\014)Tj /F7 1 Tf -0.5912 0 TD 0.382 Tc (XX)Tj /F6 1 Tf 1.9942 0 TD 0.28 Tc (\2118)Tj /F10 1 Tf -0.8618 0.02 TD 0 Tc (%)Tj /F3 1 Tf 12 0 0 12 143.13 124.05 Tm -0.003 Tc 0.053 Tw [(are adj)-15(acent)-5( i)-5(f)0( t)-5(h)-3(e)-9(r)0(e i)-5(s)-4( )-10(a )-10(p)-13(a)1(t)-5(h)-3( )]TJ /T69 1 Tf 8.391 0 0 8.391 301.77 120.21 Tm 0 Tc 0 Tw (\020)Tj 8.2521 -0.0143 TD (\022)Tj /F9 1 Tf 12.024 0 0 12.024 290.49 124.05 Tm 0.917 Tc [(\010\014)-120(\014)-460(\011)]TJ /T67 1 Tf 8.391 0 0 8.391 370.89 128.85 Tm 0 Tc (M)Tj ET q 1 i 333.45 129.69 16.8 -13.68 re W* n BT 8.391 0 0 8.391 333.45 119.97 Tm (+)Tj ET Q BT /F7 1 Tf 12.024 0 0 12.024 294.81 124.05 Tm 2.084 Tc (TT)Tj ET q 1 i 349.77 136.05 31.8 -18.12 re W* n BT /F6 1 Tf 12.024 0 0 12.024 349.77 124.05 Tm 0.276 Tc (\2074)Tj ET Q BT /F10 1 Tf 12.024 0 0 12.024 310.17 124.05 Tm 0 Tc (K)Tj /F3 1 Tf 12 0 0 12 381.57 124.05 Tm 0.06 Tw [( from )]TJ /F7 1 Tf 2.79 0 TD 0 Tw (X)Tj /F3 1 Tf 0.94 0 TD 0.001 Tc 0.059 Tw [( to )]TJ /F7 1 Tf 11.931 0 0 11.931 445.77 124.05 Tm 0 Tc 0 Tw (X)Tj /F10 1 Tf 0.1307 0.0101 TD (%)Tj /F3 1 Tf 12 0 0 12 457.05 124.05 Tm -0.002 Tc 0.062 Tw [( such t)-4(h)-2(at)-4( for)]TJ -30.58 -1.67 TD 0.002 Tc [(a)6(ll )]TJ /T70 1 Tf 8.355 0 0 8.355 140.01 100.05 Tm 0 Tc 0 Tw (\022)Tj /F7 1 Tf 11.975 0 0 11.975 108.45 104.01 Tm (X)Tj /F6 1 Tf 0.9821 0 TD 0.29 Tc (\2118)Tj /F10 1 Tf -0.8318 0.5512 TD 0 Tc (\))Tj /F3 1 Tf 12 0 0 12 146.85 104.01 Tm -0.001 Tc 0.061 Tw [( and )]TJ /F9 1 Tf 11.97 0 0 11.97 174.21 104.01 Tm 0 Tc 0 Tw (\020)Tj /F5 1 Tf 1.8647 0 TD 1.485 Tc (K+)Tj /F6 1 Tf -1.0527 0 TD 1.155 Tc (\035\035)Tj /F3 1 Tf 12 0 0 12 233.61 104.01 Tm 0 Tc (, )Tj /T67 1 Tf 8.391 0 0 8.391 249.33 99.93 Tm (K)Tj /F7 1 Tf 12.024 0 0 12.024 242.73 104.01 Tm 1.824 Tc (TX)Tj /F6 1 Tf 1.3673 0 TD 0 Tc (\212)Tj /F10 1 Tf 1.1777 0.5489 TD (\))Tj /F3 1 Tf 12 0 0 12 282.33 104.01 Tm -0.002 Tc 0.072 Tw [(. )10(For ex)-12(am)-4(pl)-4(e, )10(i)-4(n)-2( t)-4(h)-2(e fi)-4(g)8(u)-2(re, )]TJ /F9 1 Tf 13.09 0 TD 0 Tc 0 Tw (\014)Tj /F7 1 Tf -1.07 0 TD 0.89 Tc (XX)Tj /F3 1 Tf 2.78 0 TD -0.003 Tc 0.073 Tw [( are adj)-5(a)-9(cent)]TJ -30.82 -1.66 TD (because )Tj /T71 1 Tf 8.355 0 0 8.355 142.77 80.25 Tm 0 Tc 0 Tw (\020)Tj 3.9208 -0.0144 TD (\024)Tj /F9 1 Tf 11.97 0 0 11.97 147.33 84.09 Tm 1.073 Tc (\014\014)Tj /F7 1 Tf -0.9624 0 TD 2.156 Tc (TT)Tj /F10 1 Tf 1.3033 0 TD 0 Tc (K)Tj /F3 1 Tf 12 0 0 12 183.33 84.09 Tm -0.001 Tc 0.201 Tw [( is a path betw)-9(een them that does not pass throu)-11(g)9(h )-20(an)-21(y)19( )]TJ /F7 1 Tf 11.975 0 0 11.975 479.73 84.09 Tm 0 Tc 0 Tw (X)Tj /F6 1 Tf 0.972 0 TD 0.31 Tc (\2118)Tj /F3 1 Tf 12 0 0 12 519.09 84.09 Tm 0 Tc (.)Tj ET endstream endobj 146 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F3 38 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F10 61 0 R /F12 90 0 R /T55 147 0 R /T56 148 0 R /T57 149 0 R /T58 150 0 R /T59 151 0 R /T60 152 0 R /T61 153 0 R /T62 154 0 R /T63 155 0 R /T64 156 0 R /T65 157 0 R /T66 158 0 R /T67 159 0 R /T68 160 0 R /T69 161 0 R /T70 162 0 R /T71 163 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 164 0 obj << /Length 19228 >> stream BT /F3 1 Tf 12 0 0 12 300.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc (16)Tj -17.5 -3 TD -0.002 Tc 0.062 Tw [(Not)-4(i)-4(ce t)-4(h)-2(at)-4( eve)-8(r)-19(y)18( poi)-4(nt)-4( i)-4(n)-2( )]TJ /F9 1 Tf 11.975 0 0 11.975 238.77 704.01 Tm 0 Tc 0 Tw (<)Tj /F6 1 Tf -1.423 0 TD 1.475 Tc (88)Tj /F3 1 Tf 12 0 0 12 263.37 704.01 Tm -0.002 Tc 0.062 Tw [( i)-4(s)-3( adj)-4(acent)-4( t)-4(o)-2( ex)-12(act)-4(l)-14(y)18( t)-4(w)0(o )-10(ot)-4(h)-12(e)2(r )-10(poi)-4(nt)-4(s )-10(i)-4(n)-2( )]TJ /F6 1 Tf 11.975 0 0 11.975 473.01 704.01 Tm 0 Tc 0 Tw (8)Tj /F3 1 Tf 12 0 0 12 488.61 704.01 Tm 0.001 Tc 0.069 Tw (, while)Tj -33.21 -1.66 TD -0.001 Tw (points in )Tj /T71 1 Tf 8.355 0 0 8.355 145.41 680.25 Tm 0 Tc 0 Tw (\021)Tj /F6 1 Tf 11.975 0 0 11.975 137.13 684.09 Tm (8)Tj /F3 1 Tf 12 0 0 12 152.73 684.09 Tm -0.002 Tc 0.002 Tw [(are )-10(adj)-4(a)2(c)-8(e)2(nt)-4( t)-4(o)-2( )]TJ /F9 1 Tf 6.28 0 TD 1.97 Tc (\003\021)Tj /F5 1 Tf 0.94 0 TD 0 Tc 0 Tw (3)Tj /F6 1 Tf 0.91 0 TD (\016)Tj /F3 1 Tf 1.7 0 TD -0.001 Tc 0.001 Tw [( points \(3 in the ex)-11(ample\).)]TJ ET 1 g 1 i 372.33 557.85 m 372.81 561.69 l 374.25 565.53 l 376.41 569.13 l 379.29 572.01 l 382.65 573.93 l 386.73 575.37 l 390.81 575.85 l 394.89 575.37 l 398.73 573.93 l 402.09 572.01 l 405.21 569.13 l 407.37 565.53 l 408.57 561.69 l 409.05 557.85 l 408.57 553.77 l 407.37 549.93 l 405.21 546.57 l 402.09 543.69 l 398.73 541.53 l 394.89 540.09 l 390.81 539.61 l 386.73 540.09 l 382.65 541.53 l 379.29 543.69 l 376.41 546.57 l 374.25 549.93 l 372.81 553.77 l 372.33 557.85 l f* 0 G 2 J 0 j 0.24 w 10 M [0 0.48 ]0 d 372.33 557.85 m 372.81 561.69 l 374.25 565.53 l 376.41 569.13 l 379.29 572.01 l 382.65 573.93 l 386.73 575.37 l 390.81 575.85 l 394.89 575.37 l 398.73 573.93 l 402.09 572.01 l 405.21 569.13 l 407.37 565.53 l 408.57 561.69 l 409.05 557.85 l 408.57 553.77 l 407.37 549.93 l 405.21 546.57 l 402.09 543.69 l 398.73 541.53 l 394.89 540.09 l 390.81 539.61 l 386.73 540.09 l 382.65 541.53 l 379.29 543.69 l 376.41 546.57 l 374.25 549.93 l 372.81 553.77 l 372.33 557.85 l S 240.57 507.93 m 241.05 511.29 l 242.25 514.41 l 244.17 517.05 l 246.57 519.45 l 249.69 520.89 l 253.05 521.85 l 256.41 521.85 l 259.77 520.89 l 262.65 519.45 l 265.29 517.05 l 267.21 514.41 l 268.41 511.29 l 268.89 507.93 l 268.41 504.57 l 267.21 501.45 l 265.29 498.81 l 262.65 496.41 l 259.77 494.97 l 256.41 494.25 l 253.05 494.25 l 249.69 494.97 l 246.57 496.41 l 244.17 498.81 l 242.25 501.45 l 241.05 504.57 l 240.57 507.93 l f* 240.57 507.93 m 241.05 511.29 l 242.25 514.41 l 244.17 517.05 l 246.57 519.45 l 249.69 520.89 l 253.05 521.85 l 256.41 521.85 l 259.77 520.89 l 262.65 519.45 l 265.29 517.05 l 267.21 514.41 l 268.41 511.29 l 268.89 507.93 l 268.41 504.57 l 267.21 501.45 l 265.29 498.81 l 262.65 496.41 l 259.77 494.97 l 256.41 494.25 l 253.05 494.25 l 249.69 494.97 l 246.57 496.41 l 244.17 498.81 l 242.25 501.45 l 241.05 504.57 l 240.57 507.93 l S 181.53 569.13 m 182.01 573.21 l 183.21 577.05 l 185.37 580.41 l 188.01 583.53 l 191.37 585.93 l 195.21 587.61 l 199.29 588.33 l 203.37 588.33 l 207.45 587.61 l 211.29 585.93 l 214.65 583.53 l 217.29 580.41 l 219.45 577.05 l 220.65 573.21 l 221.13 569.13 l 220.65 565.05 l 219.45 561.21 l 217.29 557.61 l 214.65 554.73 l 211.29 552.33 l 207.45 550.65 l 203.37 549.69 l 199.29 549.69 l 195.21 550.65 l 191.37 552.33 l 188.01 554.73 l 185.37 557.61 l 183.21 561.21 l 182.01 565.05 l 181.53 569.13 l f* 181.53 569.13 m 182.01 573.21 l 183.21 577.05 l 185.37 580.41 l 188.01 583.53 l 191.37 585.93 l 195.21 587.61 l 199.29 588.33 l 203.37 588.33 l 207.45 587.61 l 211.29 585.93 l 214.65 583.53 l 217.29 580.41 l 219.45 577.05 l 220.65 573.21 l 221.13 569.13 l 220.65 565.05 l 219.45 561.21 l 217.29 557.61 l 214.65 554.73 l 211.29 552.33 l 207.45 550.65 l 203.37 549.69 l 199.29 549.69 l 195.21 550.65 l 191.37 552.33 l 188.01 554.73 l 185.37 557.61 l 183.21 561.21 l 182.01 565.05 l 181.53 569.13 l S 0.754 g 153.45 629.13 m 153.93 632.49 l 155.13 635.85 l 157.29 638.49 l 159.93 640.65 l 163.29 641.85 l 166.65 642.33 l 170.25 641.85 l 173.37 640.65 l 176.01 638.49 l 178.17 635.85 l 179.61 632.49 l 180.09 629.13 l 179.61 625.53 l 178.17 622.41 l 176.01 619.77 l 173.37 617.61 l 170.25 616.17 l 166.65 615.69 l 163.29 616.17 l 159.93 617.61 l 157.29 619.77 l 155.13 622.41 l 153.93 625.53 l 153.45 629.13 l f* 1 g 0.72 w []0 d 144.33 638.25 m 144.81 641.61 l 146.01 644.97 l 148.17 647.61 l 150.81 649.77 l 154.17 650.97 l 157.53 651.45 l 161.13 650.97 l 164.25 649.77 l 166.89 647.61 l 169.05 644.97 l 170.49 641.61 l 170.97 638.25 l 170.49 634.65 l 169.05 631.53 l 166.89 628.89 l 164.25 626.73 l 161.13 625.29 l 157.53 624.81 l 154.17 625.29 l 150.81 626.73 l 148.17 628.89 l 146.01 631.53 l 144.81 634.65 l 144.33 638.25 l b* 0.754 g 297.45 583.77 m 297.93 587.13 l 299.13 590.49 l 301.29 593.13 l 303.93 595.29 l 307.29 596.49 l 310.65 596.97 l 314.25 596.49 l 317.37 595.29 l 320.01 593.13 l 322.17 590.49 l 323.61 587.13 l 324.09 583.77 l 323.61 580.17 l 322.17 577.05 l 320.01 574.41 l 317.37 572.25 l 314.25 570.81 l 310.65 570.33 l 307.29 570.81 l 303.93 572.25 l 301.29 574.41 l 299.13 577.05 l 297.93 580.17 l 297.45 583.77 l f* 1 g 288.33 592.89 m 288.81 596.25 l 290.01 599.61 l 292.17 602.25 l 294.81 604.41 l 298.17 605.61 l 301.53 606.09 l 305.13 605.61 l 308.25 604.41 l 310.89 602.25 l 313.05 599.61 l 314.49 596.25 l 314.97 592.89 l 314.49 589.29 l 313.05 586.17 l 310.89 583.53 l 308.25 581.37 l 305.13 579.93 l 301.53 579.45 l 298.17 579.93 l 294.81 581.37 l 292.17 583.53 l 290.01 586.17 l 288.81 589.29 l 288.33 592.89 l b* 0.754 g 297.45 475.77 m 297.93 479.13 l 299.13 482.49 l 301.29 485.13 l 303.93 487.29 l 307.29 488.49 l 310.65 488.97 l 314.25 488.49 l 317.37 487.29 l 320.01 485.13 l 322.17 482.49 l 323.61 479.13 l 324.09 475.77 l 323.61 472.17 l 322.17 469.05 l 320.01 466.41 l 317.37 464.25 l 314.25 462.81 l 310.65 462.33 l 307.29 462.81 l 303.93 464.25 l 301.29 466.41 l 299.13 469.05 l 297.93 472.17 l 297.45 475.77 l f* 1 g 288.33 484.89 m 288.81 488.25 l 290.01 491.61 l 292.17 494.25 l 294.81 496.41 l 298.17 497.61 l 301.53 498.09 l 305.13 497.61 l 308.25 496.41 l 310.89 494.25 l 313.05 491.61 l 314.49 488.25 l 314.97 484.89 l 314.49 481.29 l 313.05 478.17 l 310.89 475.53 l 308.25 473.37 l 305.13 471.93 l 301.53 471.45 l 298.17 471.93 l 294.81 473.37 l 292.17 475.53 l 290.01 478.17 l 288.81 481.29 l 288.33 484.89 l b* 0.754 g 441.45 629.13 m 441.93 632.49 l 443.13 635.85 l 445.29 638.49 l 447.93 640.65 l 451.29 641.85 l 454.65 642.33 l 458.25 641.85 l 461.37 640.65 l 464.01 638.49 l 466.17 635.85 l 467.61 632.49 l 468.09 629.13 l 467.61 625.53 l 466.17 622.41 l 464.01 619.77 l 461.37 617.61 l 458.25 616.17 l 454.65 615.69 l 451.29 616.17 l 447.93 617.61 l 445.29 619.77 l 443.13 622.41 l 441.93 625.53 l 441.45 629.13 l f* 1 g 432.33 638.25 m 432.81 641.61 l 434.01 644.97 l 436.17 647.61 l 438.81 649.77 l 442.17 650.97 l 445.53 651.45 l 449.13 650.97 l 452.25 649.77 l 454.89 647.61 l 457.05 644.97 l 458.49 641.61 l 458.97 638.25 l 458.49 634.65 l 457.05 631.53 l 454.89 628.89 l 452.25 626.73 l 449.13 625.29 l 445.53 624.81 l 442.17 625.29 l 438.81 626.73 l 436.17 628.89 l 434.01 631.53 l 432.81 634.65 l 432.33 638.25 l b* 157.53 624.81 m 165.45 616.41 l 169.77 611.61 m 177.69 603.21 l 182.25 598.41 m 190.17 590.01 l 194.49 585.21 m 202.41 576.81 l 206.73 572.01 m 214.65 563.61 l 219.21 558.81 m 227.13 550.41 l 231.45 545.61 m 239.37 537.21 l 243.93 532.41 m 251.85 524.01 l 256.17 519.21 m 264.09 510.81 l 268.41 506.01 m 276.33 497.61 l 280.89 493.05 m 288.33 484.89 l 157.53 651.45 m 169.05 651.45 l 175.53 651.45 m 187.05 651.45 l 193.53 651.45 m 205.05 651.45 l 211.53 651.45 m 223.05 651.45 l 229.53 651.45 m 241.05 651.45 l 247.53 651.45 m 259.05 651.45 l 265.53 651.45 m 277.05 651.45 l 283.53 651.45 m 295.05 651.45 l 301.53 651.45 m 313.05 651.45 l S q 312.33 654.09 26.04 -9.96 re W* n 319.53 651.45 m 331.05 651.45 l S Q q 330.33 654.09 26.04 -9.96 re W* n 337.53 651.45 m 349.05 651.45 l S Q 355.53 651.45 m 367.05 651.45 l 373.53 651.45 m 385.05 651.45 l 391.53 651.45 m 403.05 651.45 l 409.53 651.45 m 421.05 651.45 l 427.53 651.45 m 439.05 651.45 l 445.53 624.81 m 437.61 616.41 l 433.29 611.61 m 425.37 603.21 l 421.05 598.41 m 413.13 590.01 l 408.57 585.21 m 400.65 576.81 l 396.33 572.01 m 388.41 563.61 l 384.09 558.81 m 376.17 550.41 l 371.61 545.61 m 363.69 537.21 l 359.37 532.41 m 351.45 524.01 l 347.13 519.21 m 339.21 510.81 l 334.65 506.01 m 326.73 497.61 l 322.41 492.81 m 314.97 484.89 l 170.97 638.25 m 181.77 634.17 l 187.77 631.77 m 198.57 627.69 l 204.57 625.29 m 215.37 621.21 l 221.37 618.81 m 232.17 614.73 l 238.17 612.33 m 248.97 608.25 l 254.97 605.85 m 265.77 601.53 l 271.77 599.37 m 282.57 595.05 l 314.97 592.89 m 325.77 596.97 l 331.77 599.37 m 342.57 603.45 l 348.57 605.85 m 359.37 609.93 l 365.37 612.33 m 376.17 616.41 l 382.17 618.81 m 392.97 622.89 l 398.97 625.29 m 409.77 629.61 l 415.77 631.77 m 426.57 636.09 l 301.53 579.45 m 301.53 567.93 l 301.53 561.45 m 301.53 549.93 l 301.53 543.45 m 301.53 531.93 l 301.53 525.45 m 301.53 513.93 l 301.53 507.45 m 301.53 498.09 l S BT /T72 1 Tf 8.289 0 0 8.289 217.89 565.29 Tm 0 g 0 Tc 0 Tw (\020)Tj /F7 1 Tf 11.88 0 0 11.88 211.05 569.13 Tm (T)Tj /T73 1 Tf 8.289 0 0 8.289 229.17 553.05 Tm (\021)Tj /F7 1 Tf 11.88 0 0 11.88 222.81 556.89 Tm (T)Tj /T73 1 Tf 8.289 0 0 8.289 242.01 540.81 Tm (\022)Tj /F7 1 Tf 11.88 0 0 11.88 235.29 544.65 Tm (T)Tj /T74 1 Tf 8.414 0 0 8.414 254.49 525.93 Tm (\023)Tj /F7 1 Tf 12.06 0 0 12.06 247.53 529.89 Tm (T)Tj /T75 1 Tf 8.414 0 0 8.414 265.29 513.33 Tm (\024)Tj /F7 1 Tf 12.06 0 0 12.06 258.33 517.41 Tm (T)Tj /T76 1 Tf 8.309 0 0 8.309 198.21 564.81 Tm (X)Tj /F7 1 Tf 11.904 0 0 11.904 190.53 560.13 Tm (X)Tj /T77 1 Tf 8.445 0 0 8.445 254.37 506.37 Tm (Y)Tj /F7 1 Tf 12.096 0 0 12.096 246.81 501.57 Tm (X)Tj /T76 1 Tf 8.309 0 0 8.309 396.21 551.37 Tm (Z)Tj /F7 1 Tf 11.904 0 0 11.904 388.41 546.69 Tm (X)Tj /T78 1 Tf 8.391 0 0 8.391 155.97 637.65 Tm (!)Tj /F5 1 Tf 12.027 0 0 12.027 150.33 632.85 Tm (S)Tj /T78 1 Tf 8.391 0 0 8.391 443.97 636.45 Tm (")Tj /F5 1 Tf 12.027 0 0 12.027 438.33 631.65 Tm (S)Tj /T79 1 Tf 8.391 0 0 8.391 298.89 484.53 Tm ($)Tj /F5 1 Tf 12.027 0 0 12.027 293.13 479.73 Tm (S)Tj /T79 1 Tf 8.391 0 0 8.391 299.13 591.33 Tm (#)Tj /F5 1 Tf 12.027 0 0 12.027 294.33 586.53 Tm (S)Tj /T80 1 Tf 8.309 0 0 8.309 377.97 558.81 Tm (Z)Tj /F7 1 Tf 11.904 0 0 11.904 370.65 554.13 Tm (T)Tj /T81 1 Tf 8.391 0 0 8.391 389.85 572.37 Tm (:)Tj /F7 1 Tf 12.027 0 0 12.027 382.65 567.57 Tm (T)Tj /F3 1 Tf 12 0 0 12 126.09 437.97 Tm -0.001 Tc 0.061 Tw [(F)5(o)-1(r )10(an)-21(y)19( two points )]TJ /T82 1 Tf 8.355 0 0 8.355 268.17 434.01 Tm 0 Tc 0 Tw (\021)Tj /F9 1 Tf 11.975 0 0 11.975 231.93 437.97 Tm (\014)Tj /F7 1 Tf -0.5912 0 TD 0.382 Tc (XX)Tj /F6 1 Tf 1.9942 0 TD 0.28 Tc (\2118)Tj /F10 1 Tf -0.8618 0.02 TD 0 Tc (%)Tj /F3 1 Tf 12 0 0 12 275.25 437.97 Tm -0.002 Tc 0.062 Tw [(, t)-4(h)-2(ere i)-4(s)-3( a uni)-4(que sequ)-12(ence )]TJ /T83 1 Tf 8.391 0 0 8.391 424.65 434.13 Tm 0 Tc 0 Tw (\020)Tj 7.68 -0.0143 TD (\022)Tj /F9 1 Tf 12.024 0 0 12.024 428.97 437.97 Tm 1.027 Tc (\014\014)Tj /T84 1 Tf 8.391 0 0 8.391 456.93 433.89 Tm 0 Tc (+)Tj /F7 1 Tf 12.024 0 0 12.024 417.09 437.97 Tm 2.085 Tc (XX)Tj /F6 1 Tf 4.3414 0 TD 0.286 Tc (\2118)Tj /F10 1 Tf -3.024 0 TD 0 Tc (K)Tj /F3 1 Tf 12 0 0 12 496.41 437.97 Tm -0.002 Tc 0.062 Tw [( such)]TJ -33.86 -1.67 TD 0.001 Tc [(tha)5(t)-1( )]TJ /T85 1 Tf 8.355 0 0 8.355 121.29 414.09 Tm 0 Tc 0 Tw (\020)Tj /F7 1 Tf 11.97 0 0 11.97 113.73 417.93 Tm 1.906 Tc (XX)Tj /F6 1 Tf 1.4036 0 TD 0 Tc (\036)Tj /F3 1 Tf 12 0 0 12 155.13 417.93 Tm (, )Tj /T86 1 Tf 8.355 0 0 8.355 171.09 413.73 Tm (+)Tj /F7 1 Tf 11.975 0 0 11.975 163.77 417.81 Tm 2.016 Tc (XX)Tj /F6 1 Tf 1.6435 0 TD 0 Tc (\211)Tj /F10 1 Tf 1.1224 0.02 TD (%)Tj /F3 1 Tf 12 0 0 12 206.13 417.93 Tm -0.001 Tc 0.001 Tw ( and )Tj /T87 1 Tf 8.391 0 0 8.391 267.57 413.85 Tm 0 Tc 0 Tw (\021)Tj /F9 1 Tf 12.028 0 0 12.028 244.05 417.93 Tm (\014)Tj /T88 1 Tf 8.391 0 0 8.391 239.25 413.85 Tm 1.553 Tc (KK)Tj /F7 1 Tf 12.028 0 0 12.028 232.05 417.93 Tm 0.787 Tc (XX)Tj /T89 1 Tf 8.391 0 0 8.391 261.21 413.85 Tm 0 Tc (\014)Tj /F3 1 Tf 12 0 0 12 274.41 417.93 Tm -0.003 Tc 0.003 Tw [( are )-10(adj)-5(a)1(c)-9(e)1(nt)-5(. Fo)-13(r ea)-9(ch )]TJ /F5 1 Tf 9.45 0 TD 0 Tc 0 Tw (K)Tj /F3 1 Tf 0.83 0 TD -0.001 Tc 0.001 Tw ( define)Tj ET 0.588 w 177.09 388.89 m 183.09 388.89 l S BT /T90 1 Tf 8.363 0 0 8.363 368.01 398.37 Tm 0 Tc 0 Tw (\021)Tj -6.3853 -1.3775 TD 12.866 Tc (\021\021)Tj -5.9118 -0.1865 TD 12.809 Tc (\021\021)Tj /F9 1 Tf 11.983 0 0 11.983 182.85 390.93 Tm 0.581 Tc [(\010\014)-140(\014)-30(\011)-3926(\010)-381(\014)-1392(\011)-4717(\010)-381(\014)-1432(\011)]TJ /T91 1 Tf 8.363 0 0 8.363 254.37 398.37 Tm 11.489 Tc (K+)Tj 4.0751 -1.3488 TD 13.012 Tc (JJ)Tj 1.9802 -0.0287 TD (JJ)Tj -5.9549 -0.1865 TD 11.634 Tc [(JJ)10733(K)]TJ /F5 1 Tf 11.983 0 0 11.983 176.73 390.93 Tm 2.424 Tc [(RK)-2083(R)-6439(R)]TJ /F7 1 Tf 0.8913 0 TD 0.752 Tc [(X)371(X)-5388(XX)-6549(XX)]TJ /T92 1 Tf 8.363 0 0 8.363 362.01 398.37 Tm 0 Tc (\016)Tj -6.3997 -1.3775 TD 12.562 Tc (\016\014)Tj -5.9262 -0.1865 TD 11.141 Tc [(\036\036)10546(\014)]TJ /F6 1 Tf 11.983 0 0 11.983 225.33 390.93 Tm 7.638 Tc (\036\014)Tj 17.974 0 0 17.974 238.89 388.17 Tm 4.72 Tc (\234\234)Tj /F10 1 Tf 11.983 0 0 11.983 200.97 391.05 Tm 0 Tc (%)Tj /F3 1 Tf 12 0 0 12 90.09 357.93 Tm -0.001 Tc 0.401 Tw (and define )Tj ET 155.97 356.01 m 161.97 356.01 l 235.41 356.01 m 241.41 356.01 l S BT /F9 1 Tf 12.024 0 0 12.024 161.73 357.93 Tm 0.578 Tc [(\010\014)-190(\011)-828(M)589(I)570(N)-550(\010\014)-140(\014)-30(\011)]TJ /T93 1 Tf 8.391 0 0 8.391 227.49 353.85 Tm 0 Tc 0 Tw (K)Tj /F5 1 Tf 12.024 0 0 12.024 155.61 357.93 Tm 6.187 Tc [(RR)3773(K)]TJ /F7 1 Tf 0.8882 0 TD 0.378 Tc [(XX)-4611(XX)]TJ /F6 1 Tf 2.3054 0 TD 0 Tc (\036)Tj /F10 1 Tf -1.1777 0.01 TD 6.108 Tc (%%)Tj /F3 1 Tf 12 0 0 12 282.93 357.93 Tm 0.001 Tc 0.399 Tw [(. Note)5( tha)5(t)-1( )]TJ ET 353.73 356.01 m 359.73 356.01 l 405.69 356.01 m 411.69 356.01 l S q 359.61 369.93 83.16 -18 re W* n BT /F9 1 Tf 12 0 0 12 359.61 357.93 Tm 0.57 Tc [(\010\014)-200(\011)-1360(\010)0(\014)-200(\011)]TJ ET Q q 353.37 369.93 76.08 -18 re W* n BT /F5 1 Tf 12 0 0 12 353.37 357.93 Tm 3.91 Tc (RR)Tj ET Q q 364.05 369.93 78.72 -18 re W* n BT /F7 1 Tf 12 0 0 12 364.05 357.93 Tm 0.38 Tc [(XX)-2330(XX)]TJ ET Q BT /F6 1 Tf 12 0 0 12 391.77 357.93 Tm 0 Tc 0 Tw (\036)Tj ET q 377.61 369.93 64.08 -18 re W* n BT /F10 1 Tf 12 0 0 12 377.61 358.17 Tm 2.831 Tc (%%)Tj ET Q BT /F3 1 Tf 12 0 0 12 442.77 357.93 Tm -0.002 Tc 0.402 Tw (. The )Tj /F8 1 Tf 3.11 0 TD 0.001 Tc [(modifie)5(d)]TJ -32.5 -1.67 TD 0 Tc (resistance)Tj /F3 1 Tf 4.05 0 TD 0.001 Tc -0.001 Tw ( is )Tj ET 254.49 335.97 m 260.49 335.97 l S BT /F9 1 Tf 12 0 0 12 155.97 338.13 Tm 0 Tc 0 Tw (e)Tj 0.37 -0.02 TD 0.58 Tc [(\010\014)-190(\011)-1240(\010)0(\014)-190(\011)-1110(\010\014)-180(\011)]TJ /F5 1 Tf -0.47 0 TD 3.82 Tc [(RR)200(R)]TJ /F7 1 Tf 0.85 0 TD 0.38 Tc [(XX)-2230(XX)-2090(XX)]TJ /F6 1 Tf 2.31 0 TD 3.346 Tc (\036\016)Tj /F10 1 Tf -1.18 0.02 TD 3.731 Tc [(%%)140(%)]TJ /F11 1 Tf -7.37 -2.18 TD -0.001 Tc 0.061 Tw [(Theore)-7(m)12( 6.2:)]TJ /F8 1 Tf 5.77 0 TD 0 Tc 0.06 Tw [( )-10(W)13(ith unlikel)-12(y innovation )]TJ /F9 1 Tf 11.36 0 TD 0.63 Tc [(\010\011)-730(\020)]TJ /F7 1 Tf -0.56 0 TD 0.34 Tc (NX)Tj ET q 315.57 323.97 21.72 -18 re W* n BT /F6 1 Tf 12 0 0 12 315.57 311.97 Tm 0 Tc 0 Tw (\037)Tj ET Q BT /F8 1 Tf 12 0 0 12 337.29 311.97 Tm 0 Tc 0.07 Tw [( )10(if and only if )]TJ /F7 1 Tf 6.15 0 TD 0 Tw (X)Tj /F8 1 Tf 0.94 0 TD 0.07 Tw [( is the root of a tree)]TJ -27.69 -1.67 TD 0.001 Tc -0.001 Tw [(with le)5(ast modifie)5(d re)5(sistanc)5(e)5( in )]TJ /T94 1 Tf 8.355 0 0 8.355 258.69 287.97 Tm 0 Tc 0 Tw (\021)Tj /F6 1 Tf 11.975 0 0 11.975 250.65 291.93 Tm (8)Tj /F8 1 Tf 12 0 0 12 265.41 291.93 Tm (.)Tj -14.61 -2.17 TD -0.001 Tc (Proof: )Tj /F3 1 Tf 2.87 0 TD 0.001 Tw [(I)22(n)-1( )-10(Appendix)-11( B)6(.)]TJ /F12 1 Tf 32.24 -1.66 TD 0 Tc 0 Tw (\346)Tj /F1 1 Tf 14.04 0 0 14.04 90.09 213.93 Tm -0.002 Tc 0.006 Tw [(7.)-6( The Conti)-6(nuous )-9(A)19(ppr)-6(oxi)-6(mati)-6(on)]TJ /F3 1 Tf 12 0 0 12 126.09 190.89 Tm 0.001 Tc 0.049 Tw [(I)14(n)1( ma)5(n)-19(y)21( )-10(a)5(pplic)5(a)5(tions it is use)5(f)4(ul to think of )]TJ /F5 1 Tf 18.09 0 TD 0 Tc 0 Tw (M)Tj /F3 1 Tf 1.16 0 TD -0.001 Tc 0.061 Tw [( )10(as bein)-11(g)9( lar)-8(g)9(e, )-10(as round-of)-8(f e)-7(rror)]TJ -22.25 -1.66 TD 0.001 Tc 0.079 Tw [(on )10(the)5( )10(g)11(r)4(id )10(is )10(not )10(usua)5(ll)-21(y)21( )10(of )10(muc)5(h)1( )-10(e)5(c)5(onomic)5( inte)5(re)5(st. This le)5(a)5(d)1(s us to de)5(fine)5( cost a)5(s)0( the)]TJ 0 -1.67 TD -0.001 Tc 0.061 Tw [(limit of per capita modified resistan)-11(ce. Most results )-10(about )-10(modified )-10(r)-8(e)3(sistance )-10(then )-10(h)-11(a)3(ve)]TJ T* 0.001 Tw [(an anal)-3(o)-11(g)9( i)-3(n)-1( t)-3(e)3(rm)-3(s of )-10(cost)-3(.)]TJ 3 -1.66 TD 0 Tc 0.21 Tw (Suppose that )Tj /F9 1 Tf 6.37 0 TD 0 Tw (\014)Tj /F5 1 Tf -0.4 0 TD 0.339 Tc [(SS)-1040(3)]TJ /F6 1 Tf 1.6 0 TD 0 Tc (\211)Tj /F10 1 Tf -0.78 0.03 TD (%)Tj /F3 1 Tf 2.69 -0.03 TD -0.001 Tc 0.211 Tw [(. As we did ea)-7(rlier, for )]TJ /F9 1 Tf 12.028 0 0 12.028 368.85 110.97 Tm 3.288 Tc (\020\021)Tj /F5 1 Tf 1.8656 0 TD 0 Tc 0 Tw (X)Tj /F6 1 Tf -1.0575 0 TD 1.167 Tc (bb)Tj /F3 1 Tf 12 0 0 12 423.21 110.97 Tm 0 Tc 0.22 Tw [( )10(de)4(fine)4( a)4( fa)4(mily)10( )-10(of)]TJ -27.76 -1.67 TD 0.001 Tc -0.001 Tw [(mix)-9(e)5(d)1( stra)5(te)5(g)11(i)-1(e)5(s)0( )]TJ /F9 1 Tf 7.55 0 TD 0.5 Tc (\010\011)Tj /F5 1 Tf 0.34 0 TD 0 Tc 0 Tw (X)Tj /F7 1 Tf -0.91 0 TD (T)Tj /F3 1 Tf 2.05 0 TD 0.01 Tc -0.01 Tw [( by)30( )]TJ /F9 1 Tf 2.27 0 TD 0.5 Tc [(\010\011)500(;)50(=)-1350(\014)-170(\010)0(\011)500(;)-10(=)-810(\021)]TJ /F5 1 Tf 0.34 0 TD 0.701 Tc [(XS)-1018(X)-620(X)-10(S)-2668(X)]TJ /F7 1 Tf -0.91 0 TD 4.529 Tc (TT)Tj /F6 1 Tf 3.11 0 TD 4.376 Tc [(\036\036)3410(\016)]TJ /F10 1 Tf 4.14 0.03 TD 0 Tc 0 Tw (%)Tj /F3 1 Tf 4.55 -0.03 TD 0.001 Tc -0.001 Tw [(. Conside)5(r)4( the)5( utilit)-11(y)31( diffe)5(r)4(e)5(n)-9(c)5(e)]TJ ET endstream endobj 165 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F1 36 0 R /F3 38 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F10 61 0 R /F11 62 0 R /F12 90 0 R /T71 163 0 R /T72 166 0 R /T73 167 0 R /T74 168 0 R /T75 169 0 R /T76 170 0 R /T77 171 0 R /T78 172 0 R /T79 173 0 R /T80 174 0 R /T81 175 0 R /T82 176 0 R /T83 177 0 R /T84 178 0 R /T85 179 0 R /T86 180 0 R /T87 181 0 R /T88 182 0 R /T89 183 0 R /T90 184 0 R /T91 185 0 R /T92 186 0 R /T93 187 0 R /T94 188 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 189 0 obj << /Length 8825 >> stream BT /F3 1 Tf 12 0 0 12 300.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc (17)Tj /F9 1 Tf -5.24 -2.67 TD 0.5 Tc [(\010\011)-1410(\010)170(\014)-170(\010\011)500(\011)-1170(\010)110(\014)-480(\010)0(\011)500(\011)]TJ /F5 1 Tf -0.84 0 TD 0.44 Tc [(5X)-1391(U)120(S)-849(X)-1551(U)120(S)-1219(X)]TJ /F7 1 Tf 5.14 0 TD 4.809 Tc (TT)Tj /F6 1 Tf -2.74 0 TD 4.366 Tc [(\036\016)2526(\011)]TJ /F10 1 Tf 7.03 0.03 TD 0 Tc 0 Tw (%)Tj /F3 1 Tf 3.52 -0.03 TD (.)Tj -24.37 -2.33 TD -0.001 Tc (Define)Tj /F6 1 Tf 11.916 0 0 24.813 289.53 647.73 Tm 16.093 Tc (\\^)Tj /T95 1 Tf 8.355 0 0 8.355 172.05 660.69 Tm 28.058 Tc (\021\021)Tj -0.359 -2.0968 TD 15.707 Tc (\020\020)Tj /F9 1 Tf 11.97 0 0 11.97 120.69 650.97 Tm -0.109 Tc [(\010)-441(\014)-681(\011)-2847(\021)0(\010)-772(\010)-611(\011)-1473(\020)-67(\011)-2306(M)-112(I)-109(N)-2708(\021\010)-772(\010)-611(\011)-1473(\020)-77(\011)-3679(\021\010)-772(\010)-611(\011)-1473(\020)-77(\011)]TJ /T96 1 Tf 8.355 0 0 8.355 307.77 660.69 Tm 0 Tc (Y)Tj -3.0303 -1.4505 TD (Y)Tj 14.9363 -0.6463 TD (Y)Tj /F5 1 Tf 11.97 0 0 11.97 115.29 650.97 Tm 2.569 Tc [(C)2258(S)2228(S)-1241(5)2116(XD)2559(X)-3619(5)2116(XD)2559(X)-742(5)2116(XD)2569(X)]TJ /F6 1 Tf 2.7069 0 TD 4.652 Tc [(w\035)2284(\016)-2829(\035)2244(\014)108(\037)]TJ 17.955 0 0 17.955 161.49 646.77 Tm 7.125 Tc [(\250\250)1798(\250)]TJ /F10 1 Tf 11.97 0 0 11.97 134.37 651.33 Tm 0 Tc (%)Tj /F3 1 Tf 12 0 0 12 495.57 650.97 Tm (.)Tj -33.79 -2.91 TD -0.002 Tc 0.002 Tw [( F)4(o)-2(r an)-22(y)18( pu)-12(re pro)-12(f)1(ile )]TJ /F5 1 Tf 8.69 0 TD 0 Tc 0 Tw (S)Tj /F3 1 Tf 0.76 0 TD 0.002 Tc -0.002 Tw [( le)6(t )]TJ /F9 1 Tf 2.38 0 TD 0.37 Tc (\010\011)Tj /F5 1 Tf -0.8 0 TD 0.39 Tc (4S)Tj /F3 1 Tf 2.17 0 TD -0.001 Tc 0.001 Tw ( be all trees on )Tj /F5 1 Tf 6.25 0 TD 0 Tc 0 Tw (3)Tj /F3 1 Tf 0.91 0 TD ( with root )Tj /F5 1 Tf 4.3 0 TD (S)Tj /F3 1 Tf 0.76 0 TD (.)Tj /T97 1 Tf 8.379 0 0 8.379 301.65 587.37 Tm 0.439 Tc (\010\011)Tj /F9 1 Tf 12 0 0 12 229.89 592.17 Tm 0 Tc (e)Tj 0.36 -0.02 TD 0.38 Tc [(\010\011)-1030(M)389(I)371(N)-4261(\010)0(\014)-250(\010)-50(\011)380(\011)]TJ /T98 1 Tf 8.379 0 0 8.379 294.69 587.37 Tm 0.45 Tc (4S)Tj 4.1963 -0.1289 TD 0 Tc (S)Tj /F5 1 Tf 12 0 0 12 228.69 591.93 Tm 0.309 Tc [(CS)-7400(C)10(S)-960(S)]TJ /T99 1 Tf 8.379 0 0 8.379 285.33 587.37 Tm 0 Tc (U)Tj /F7 1 Tf 12 0 0 12 354.93 591.93 Tm (U)Tj /T100 1 Tf 8.379 0 0 8.379 290.13 587.37 Tm (\211)Tj /F6 1 Tf 12 0 0 12 251.49 591.93 Tm (\036)Tj 18 0 0 18 314.49 589.17 Tm (\234)Tj /T101 1 Tf 8.379 0 0 8.379 330.45 586.65 Tm (%)Tj ET q 1 i 345.33 605.97 36.72 -19.92 re W* n BT /F10 1 Tf 12 0 0 12 345.33 592.29 Tm 1.181 Tc (%%)Tj ET Q BT /F3 1 Tf 12 0 0 12 382.05 591.93 Tm (.)Tj -21.33 -2.65 TD [(W)-6(e)4( first establish the relationship between modified )-10(resistanc)-6(e)4( and )-10(cost.)]TJ /F11 1 Tf -3 -2.17 TD -0.001 Tc 0.001 Tw [(Theore)-7(m)12( 7.1:)]TJ /F8 1 Tf 5.71 0 TD 0 Tc 0 Tw ( )Tj ET 0 G 2 J 0 j 0.588 w 10 M []0 d 1 i 209.13 532.17 m 215.13 532.17 l S BT /F9 1 Tf 12 0 0 12 164.37 534.09 Tm 0.33 Tc [(L)331(I)331(M)-2491(\010\014)-240(\011)260(\017)-2480(\010\014)-240(\011)]TJ /T102 1 Tf 8.379 0 0 8.379 181.17 531.69 Tm 0 Tc (M)Tj /F5 1 Tf 12 0 0 12 208.77 534.09 Tm 0.41 Tc [(RS)71(S)-729(M)-1040(C)111(S)71(S)]TJ /T103 1 Tf 8.379 0 0 8.379 188.85 531.69 Tm 0.031 Tc (ld)Tj /F6 1 Tf 12 0 0 12 260.97 534.09 Tm 0 Tc (\036)Tj /F10 1 Tf -2.7 0.03 TD 4.831 Tc (%%)Tj /F8 1 Tf 6.35 -0.03 TD 0 Tc (.)Tj -17.89 -2.17 TD (Proof:)Tj /F3 1 Tf 2.61 0 TD 0.001 Tc -0.001 Tw [( F)7(o)1(llows from integ)11(r)-6(a)5(tion the)5(o)1(r)-16(y)21( a)5(nd the)5( d)-9(e)5(finitions.)]TJ /F12 1 Tf 32.5 -1.66 TD 0 Tc 0 Tw (\346)Tj /F3 1 Tf -35.11 -1.67 TD [(The most useful application of Th)-10(eorem 7.1 is throu)-10(g)10(h an obvious co)-10(rollar)-17(y)20(.)]TJ /F11 1 Tf 0 -2.17 TD (Corollary 7.2:)Tj /F8 1 Tf 5.99 0 TD ( If )Tj /F9 1 Tf 1.71 0 TD 0.52 Tc [(\010\011)-1210(\010\011)]TJ /F5 1 Tf -0.45 0 TD 2.569 Tc (CC)Tj /F7 1 Tf 0.83 0 TD 2.55 Tc (UU)Tj /F6 1 Tf 1.17 0 TD 0 Tc (\037)Tj /F10 1 Tf 1.94 0.03 TD (%)Tj /F8 1 Tf 1 -0.03 TD 0.001 Tc -0.001 Tw [( the)5(n)1( for all )]TJ /F5 1 Tf 5.11 0 TD 0 Tc 0 Tw (M)Tj /F8 1 Tf 1.16 0 TD 0.001 Tc -0.001 Tw [( suffic)5(ie)5(ntly)5( large)5(,)1( )]TJ /F9 1 Tf 7.77 0.02 TD 2.57 Tc (ee)Tj 0.37 -0.02 TD 0.52 Tc [(\010\011)-1260(\010\011)]TJ /F5 1 Tf -0.47 0 TD 2.66 Tc (RR)Tj /F7 1 Tf 0.85 0 TD 2.59 Tc (UU)Tj /F6 1 Tf 1.17 0 TD 0 Tc 0 Tw (\037)Tj /F10 1 Tf 1.98 0.03 TD (%)Tj /F8 1 Tf 1.08 -0.03 TD (.)Tj /F3 1 Tf -31.21 -2.16 TD 0.05 Tw [(This c)4(o)0(rolla)4(r)-17(y)20( me)4(a)4(n)0(s tha)4(t)-2( )-10(for )]TJ /F5 1 Tf 12.28 0 TD 0 Tw (M)Tj /F3 1 Tf 1.16 0 TD -0.002 Tc 0.062 Tw [( )10(l)-4(a)2(rge )10(t)-4(h)-2(e l)-4(east)-4( m)-4(odi)-4(fi)-4(ed )-10(resi)-4(st)-4(ance t)-14(r)1(ees )-10(are )-10(a subset)-4( of)]TJ -13.44 -1.67 TD -0.001 Tc [(the least cost trees. )-20(I)12(n)-1( particula)-7(r)2(, least cost is a n)-11(ecess)-12(a)3(r)-18(y)19( \()-8(a)3(lthoug)9(h no lon)-11(g)9(er)-8( )-10(suffici)-13(ent\))]TJ T* 0 Tc 0 Tw [(condition to be stochasticall)-12(y)20( stabl)-12(e)4(. F)6(r)3(om Th)-10(eorem 6.1, w)-8(e)4( hav)-10(e)]TJ /F11 1 Tf 0 -2.16 TD 0.07 Tw [(Corollary 7.3:)]TJ /F8 1 Tf 6.06 0 TD [( Suppose unlikely innovation and sufficiently large)]TJ /F5 1 Tf 20.87 0 TD 0 Tw (M)Tj /F8 1 Tf 1.16 0 TD 0.08 Tw (. Then )Tj /F9 1 Tf 3.69 0 TD [(\010[)-350(]\011)-1360(\020)]TJ /F5 1 Tf 0.8 0 TD 0 Tw (S)Tj /F7 1 Tf -1.36 0 TD (N)Tj /F6 1 Tf 2.94 0 TD (\037)Tj /F8 1 Tf -34.16 -1.67 TD (only if)Tj /F9 1 Tf 12.024 0 0 12.024 128.97 304.17 Tm 5.628 Tc (ee)Tj 0.3593 -0.01 TD 0.378 Tc [(\010\011)-1028(M)389(I)370(N)-1518(\010)-50(\011)]TJ /T104 1 Tf 8.391 0 0 8.391 183.93 299.97 Tm 0.767 Tc (S3)Tj /F5 1 Tf 12.024 0 0 12.024 127.77 304.05 Tm 0.307 Tc [(CS)-4641(C)-10(S)]TJ /T105 1 Tf 8.391 0 0 8.391 188.61 299.97 Tm 0 Tc (\211)Tj /F6 1 Tf 12.024 0 0 12.024 150.57 304.05 Tm (\036)Tj /T106 1 Tf 8.391 0 0 8.391 184.53 300.21 Tm (%)Tj /F10 1 Tf 12.024 0 0 12.024 211.65 304.41 Tm (%)Tj /F3 1 Tf 12 0 0 12 224.13 304.05 Tm (.)Tj -11.17 -1.66 TD 0.04 Tw [(F)6(i)-2(nall)-12(y)20(,)0( )10(b)-10(e)4(c)-6(a)4(use )10(z)-6(e)4(ro )10(cost )10(conne)-6(ction )10(pla)-16(y)20( an important )-10(role in the theor)-17(y)20(, it is important)]TJ 0 -1.67 TD -0.002 Tc 0.002 Tw [(t)-4(h)-2(at)-4( z)-8(e)2(ro cost)-4( i)-4(m)-4(p)-2(l)-4(i)-4(e)2(s z)-8(e)2(ro m)-4(odi)-4(fi)-4(ed resi)-4(st)-4(ance fo)-12(r al)-4(l)-4( suffi)-4(ci)-4(ent)-4(l)-24(y)18( l)-4(a)-8(r)-9(g)8(e )]TJ /F5 1 Tf 28.69 0 TD 0 Tc 0 Tw (M)Tj /F3 1 Tf 1.16 0 TD (.)Tj /F11 1 Tf -29.85 -2.17 TD -0.001 Tc 0.001 Tw [(Theore)-7(m)12( 7.4:)]TJ /F8 1 Tf 5.71 0 TD 0 Tc 0 Tw ( If )Tj /F9 1 Tf 1.71 0 TD 0.33 Tc [(\010\014)-250(\011)-1070(\020)]TJ /F5 1 Tf -0.45 0 TD 0.309 Tc [(CS)-30(S)]TJ /F6 1 Tf 2.7 0 TD 0 Tc (\036)Tj /F10 1 Tf -1.11 0.03 TD (%)Tj /F8 1 Tf 2.94 -0.03 TD 0.001 Tc -0.001 Tw [( the)5(n)1( for all )]TJ /F5 1 Tf 5.12 0 TD 0 Tc 0 Tw (M)Tj /F8 1 Tf 1.16 0 TD 0.001 Tc -0.001 Tw [( suffic)5(ie)5(ntly)5( large)5( )]TJ ET 393.45 236.13 m 399.45 236.13 l S BT /F9 1 Tf 12 0 0 12 399.21 238.05 Tm 0.33 Tc [(\010\014)-240(\011)-1080(\020)]TJ /F5 1 Tf -0.51 0 TD 0.41 Tc [(RS)71(S)]TJ /F6 1 Tf 2.75 0 TD 0 Tc 0 Tw (\036)Tj /F10 1 Tf -1.1 0.03 TD (%)Tj /F8 1 Tf 2.96 -0.03 TD (.)Tj -29.86 -2.16 TD -0.001 Tc (Proof: )Tj /F3 1 Tf 2.86 0 TD 0.001 Tw (To be shown.)Tj /F12 1 Tf 32.25 -1.67 TD 0 Tc 0 Tw (\346)Tj /F1 1 Tf 14.04 0 0 14.04 90.09 160.05 Tm 0.001 Tc 0.003 Tw [(8. Furthe)10(r)-3( Resu)14(lt)26(s)]TJ /F3 1 Tf 12 0 0 12 126.09 137.13 Tm -0.001 Tc 0.001 Tw [(W)-7(e)3( now g)9(i)-3(ve )-10(a more detail)-13(ed cha)-7(r)2(act)-13(eriz)-7(ation of stochasticall)-23(y)19( stable sets.)]TJ /F11 1 Tf -3 -2.17 TD 0 Tc 0 Tw [(Def)-7(i)-2(nition 8.1:)]TJ /F8 1 Tf 6.12 0 TD ( )Tj /F9 1 Tf 1 0 TD (\007)Tj /F5 1 Tf -0.6 0 TD (S)Tj /F8 1 Tf 1 0 TD 0.001 Tc -0.001 Tw ( is a )Tj /F11 1 Tf 1.92 0 TD -0.002 Tc 0.002 Tw [(stron)-6(g)-2(l)-4(y)-2( b)-6(e)2(tter )-10(resp)-6(o)-2(n)-6(s)-3(e)]TJ /F8 1 Tf 10.27 0 TD 0.001 Tc -0.001 Tw ( to )Tj /F5 1 Tf 1.44 0 TD 0 Tc 0 Tw (S)Tj /F8 1 Tf 0.76 0 TD 0.002 Tc -0.002 Tw ( if )Tj /F9 1 Tf 1.65 0 TD 0 Tc [(\010)-330(\014)-680(\007\011)-1410(\020)]TJ ET q 367.41 123.09 42.24 -18 re W* n BT /F5 1 Tf 12 0 0 12 367.41 111.09 Tm 0.309 Tc [(CS)-30(S)]TJ ET Q BT /F6 1 Tf 12 0 0 12 403.29 111.09 Tm 0 Tw (\036)Tj ET endstream endobj 190 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F1 36 0 R /F3 38 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F10 61 0 R /F11 62 0 R /F12 90 0 R /T95 191 0 R /T96 192 0 R /T97 193 0 R /T98 194 0 R /T99 195 0 R /T100 196 0 R /T101 197 0 R /T102 198 0 R /T103 199 0 R /T104 200 0 R /T105 201 0 R /T106 202 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 204 0 obj << /Length 7952 >> stream BT /F3 1 Tf 12 0 0 12 300.09 740.01 Tm 0 g BX /GS1 gs EX 0 Tc (18)Tj -17.5 -3 TD 0.25 Tw [(I)13(f)-7( )10(a pro)-10(f)3(ile admits no strong)10(l)-22(y)20( better respons)-11(e, we call it a )-10(g)10(e)4(neralized strict Nash)]TJ 0 -1.66 TD 0.001 Tc [(e)5(quilibrium.)]TJ /F11 1 Tf 0 -2.17 TD 0 Tc [(Def)-7(i)-2(nition 8.2: )]TJ /F5 1 Tf 7.02 0 TD 0 Tw (S)Tj /F8 1 Tf 0.76 0 TD 0.001 Tc 0.249 Tw [( is a )]TJ /F11 1 Tf 2.67 0 TD 0.002 Tc 0.248 Tw [(ge)6(ne)6(r)6(a)2(liz)6(e)6(d)-2( str)6(i)0(ct Nash e)6(quilibr)6(i)0(um)]TJ /F8 1 Tf 15.83 0 TD [( if )]TJ /F9 1 Tf 2.15 0 TD 0.33 Tc [(\010\014)-350(\007)320(\011)-1030(\020)]TJ /F5 1 Tf -0.45 0 TD 0.309 Tc [(CS)-30(S)]TJ /F6 1 Tf 2.96 0 TD 0 Tc 0 Tw (\037)Tj /F8 1 Tf 1.82 0 TD 0.001 Tc 0.259 Tw [( for)10( all)]TJ /F9 1 Tf -31.99 -1.67 TD 0 Tc 0 Tw (\007)Tj /F5 1 Tf -0.61 0 TD 1.769 Tc (SS)Tj /F6 1 Tf 1.12 0 TD 0 Tc (v)Tj /F8 1 Tf 1.8 0 TD (.)Tj /F3 1 Tf -3.08 -2.16 TD -0.001 Tc 0.041 Tw [(Since a strate)-7(g)-11(y)19( that do)-11(es strictl)-13(y)19( wo)-11(rse c)-7(a)3(nnot be a stron)-11(g)9(l)-23(y)19( )-10(b)-11(e)3(tter )-10(r)-8(e)3(sponse, )-10(eve)-7(r)-18(y)19( )-10(strict)]TJ 0 -1.67 TD 0.001 Tc -0.001 Tw [(Na)5(sh e)5(quilibrium is a)5( ge)5(ne)5(ra)5(lize)5(d)1( stric)5(t)-1( Na)5(sh e)5(quilibrium.)]TJ /F11 1 Tf 0 -2.17 TD 0 Tc 0 Tw [(Def)-7(i)-2(nition 8.3:)]TJ /F8 1 Tf 6.12 0 TD ( )Tj /F6 1 Tf 0.43 0 TD (4)Tj /F8 1 Tf 0.97 0 TD 0.001 Tc -0.001 Tw ( is a )Tj /F11 1 Tf 1.92 0 TD -0.003 Tc 0.003 Tw [(stron)-7(g)-3(l)-5(y)-3( b)-7(e)1(tter )-10(resp)-7(o)-3(n)-7(s)-4(e cycl)-5(e)]TJ /F8 1 Tf 12.62 0 TD 0.001 Tc -0.001 Tw ( if)Tj -22.06 -2.66 TD 0 Tc [(1\))13( )]TJ /F5 1 Tf 11.97 0 0 11.97 104.97 534.09 Tm 0 Tw (S)Tj /F6 1 Tf 0.792 0 TD 0.28 Tc (\2114)Tj /F8 1 Tf 12 0 0 12 137.01 534.09 Tm 0 Tc ( and )Tj /F9 1 Tf 2.76 0 TD (\007)Tj /F5 1 Tf -0.6 0 TD (S)Tj /F8 1 Tf 1 0 TD [( a strongly better r)-11(e)4(sponse to )]TJ /F5 1 Tf 12.37 0 TD (S)Tj /F8 1 Tf 0.76 0 TD 0.001 Tc -0.001 Tw [( impl)9(ie)5(s )]TJ /F9 1 Tf 11.97 0 0 11.97 382.29 534.09 Tm 0 Tc 0 Tw (\007)Tj /F5 1 Tf -0.6116 0 TD (S)Tj /F6 1 Tf 1.1128 0 TD 0.28 Tc (\2114)Tj /F8 1 Tf 12 0 0 12 90.09 502.05 Tm 0 Tc [(2\))13( )]TJ /F9 1 Tf 1.69 0 TD 0.68 Tc (\014\007)Tj /F5 1 Tf -0.4 0 TD 0.339 Tc (SS)Tj /F6 1 Tf 1.86 0 TD 0.278 Tc (\2114)Tj /F8 1 Tf 1.9 0 TD -0.001 Tc 0.051 Tw [( implies a sequenc)-7(e )]TJ /T107 1 Tf 8.391 0 0 8.391 260.73 498.21 Tm 0 Tc 0 Tw (\020)Tj 1.5732 -0.0143 TD (\021)Tj /F9 1 Tf 12.024 0 0 12.024 251.73 502.05 Tm 0.718 Tc [(\010\014)-70(\014)-309(\014)-449(\011)]TJ /T108 1 Tf 8.391 0 0 8.391 302.73 497.97 Tm 0 Tc (+)Tj /F5 1 Tf 12.024 0 0 12.024 255.45 502.05 Tm 0.727 Tc [(SS)-1237(S)]TJ /F10 1 Tf 2.1857 0 TD 0 Tc (K)Tj /F8 1 Tf 12 0 0 12 317.73 502.05 Tm 0.05 Tw [( such that )]TJ /T109 1 Tf 8.391 0 0 8.391 376.41 498.21 Tm 0 Tw (\020)Tj /F9 1 Tf 12.024 0 0 12.024 403.17 502.05 Tm 3.203 Tc (\014\007)Tj /T110 1 Tf 8.391 0 0 8.391 412.41 497.97 Tm 0 Tc (+)Tj ET q 1 i 371.13 514.05 79.08 -18.12 re W* n BT /F5 1 Tf 12.024 0 0 12.024 371.13 502.05 Tm 1.854 Tc [(SS)1516(S)-260(S)]TJ ET Q q 1 i 385.53 514.05 63.48 -18.12 re W* n BT /F6 1 Tf 12.024 0 0 12.024 385.53 502.05 Tm 2.509 Tc (\036\036)Tj ET Q BT /F8 1 Tf 12 0 0 12 450.21 502.05 Tm 0.06 Tw [( and )]TJ /T111 1 Tf 8.391 0 0 8.391 493.77 497.97 Tm 0 Tw (\021)Tj /T112 1 Tf -1.3587 0 TD (K)Tj /F5 1 Tf 12.028 0 0 12.028 477.57 502.05 Tm (S)Tj /T113 1 Tf 8.391 0 0 8.391 487.53 497.97 Tm (\014)Tj /F8 1 Tf 12 0 0 12 500.61 502.05 Tm 0.002 Tc 0.058 Tw [( is a)]TJ -34.21 -1.67 TD 0 Tc 0 Tw (strongly better response to )Tj /T114 1 Tf 8.391 0 0 8.391 231.21 477.93 Tm (K)Tj /F5 1 Tf 12.028 0 0 12.028 226.29 482.01 Tm (S)Tj /F11 1 Tf 12 0 0 12 90.09 450.09 Tm -0.001 Tc 0.041 Tw [(Theore)-7(m)12( 8.1:)]TJ /F8 1 Tf 5.75 0 TD [( If )]TJ /F5 1 Tf 1.36 0 TD 0 Tc 0 Tw (S)Tj /F8 1 Tf 0.76 0 TD 0.04 Tw [( is the unique long-run stationary state )-10(then )]TJ /F5 1 Tf 18.28 0 TD 0 Tw (S)Tj /F8 1 Tf 0.76 0 TD 0.05 Tw [( is a generalized strict)]TJ -26.91 -1.67 TD 0.001 Tc -0.001 Tw [(Nash e)5(quilibrium)]TJ 0 -2.17 TD 0 Tc (Proof:)Tj /F3 1 Tf 2.61 0 TD 0 Tw [( )-10(I)13(f)3( not and )]TJ /F5 1 Tf 4.55 0 TD (S)Tj /F3 1 Tf 0.76 0 TD -0.001 Tc 0.001 Tw [( is the root of a )-10(least )-10(cost )-10(tre)-7(e)3(, )-10(find )]TJ ET q 1 i 361.77 416.01 52.92 -18 re W* n BT /F9 1 Tf 12 0 0 12 361.77 404.01 Tm 0 Tc [(\010)-330(\014)-680(\007\011)-1410(\020)]TJ ET Q q 1 i 356.37 416.01 42.24 -18 re W* n BT /F5 1 Tf 12 0 0 12 356.37 404.01 Tm 0.309 Tc [(CS)-30(S)]TJ ET Q BT /F6 1 Tf 12 0 0 12 392.25 404.01 Tm 0 Tc 0 Tw (\036)Tj /F3 1 Tf 1.87 0 TD -0.001 Tc 0.011 Tw [( and paste it above the)]TJ -27.05 -1.66 TD 0 Tc (root.)Tj /F12 1 Tf 35.11 -1.67 TD 0 Tw (\346)Tj /F8 1 Tf -35.11 -1.67 TD -0.002 Tc (Remark:)Tj /F3 1 Tf 3.43 0 TD 0 Tc [( Th)-10(e sum of costs in both directions is less than or equ)-10(a)4(l one.)]TJ /F11 1 Tf -3.43 -2.16 TD -0.001 Tc 0.001 Tw [(Theore)-7(m)12( 8.2:)]TJ /F8 1 Tf 5.71 0 TD 0 Tc 0 Tw [( In a l)-12(e)4(ast cost tree )]TJ /F9 1 Tf 8.49 0 TD 0.33 Tc [(\010\014)-300(\010)-40(\011)320(\011)-960(\021)260(\017)230(\022)]TJ /F5 1 Tf -0.45 0 TD 0.309 Tc [(CS)-900(S)]TJ /F7 1 Tf 1.58 0 TD 0 Tc (U)Tj /F6 1 Tf 2.31 0 TD (b)Tj /F8 1 Tf -17.64 -2.17 TD (Proof:)Tj /F3 1 Tf 2.61 0 TD [( )-10(I)13(f)3( not cut )]TJ /F5 1 Tf 4.33 0 TD (S)Tj /F4 1 Tf 0.76 0 TD [(. Pasting)10( either abov)-10(e or below the)-6( root costs less than or )-10(equal \275.)]TJ /F12 1 Tf 27.41 -1.67 TD (\346)Tj /F4 1 Tf -35.11 -1.66 TD [(Denote the set of p)-10(a)4(irs with costs strictl)-12(y)20( b)-10(e)4(twe)-6(e)4(n z)-6(e)4(ro and one)]TJ /F9 1 Tf 13.83 -1.84 TD [([\010)-330(\014)-680(\007)0(\011)-240(\\)-220(\021)-1730(\010)-330(\014)-670(\007)-10(\011)-1360(\020)53(])]TJ /F5 1 Tf -2.18 0 TD 2.32 Tc [(0S)1981(S)-969(C)2021(S)1981(S)]TJ /F6 1 Tf 1.11 0 TD 4.536 Tc [(\036\037)1330(\037)]TJ /F4 1 Tf 11.53 0 TD 0 Tc (.)Tj /F11 1 Tf -24.29 -2.83 TD [(Assum)13(p)-4(tion 8.1 [Generic )-10(Assum)13(p)-4(tion]:)]TJ /F8 1 Tf 16.6 0 TD -0.001 Tc 0.011 Tw [( If )]TJ /T115 1 Tf 8.355 0 0 8.355 311.37 192.09 Tm 1.317 Tc [(\021\022)-3102(\021)-1608(\022)]TJ /F9 1 Tf 11.975 0 0 11.975 315.33 196.05 Tm 3.187 Tc (\014\014)Tj /F5 1 Tf -0.8618 0 TD 0.563 Tc [(00)-1132(0)161(0)-1132(0)]TJ /F6 1 Tf 2.5554 0 TD 2.635 Tc (\210v)Tj /F8 1 Tf 12 0 0 12 403.77 196.05 Tm 0.001 Tc -0.001 Tw [( the)5(n)]TJ /T116 1 Tf 6.008 0 0 6.008 274.05 157.65 Tm 11.025 Tc (\021\022)Tj /F9 1 Tf 12.018 0 0 12.018 283.89 166.05 Tm 0.539 Tc [(\010\011)-3934(\010)10(\011)]TJ /T117 1 Tf 8.386 0 0 8.386 259.29 160.41 Tm 0.709 Tc [(P0)-5621(P)14(0)]TJ /F5 1 Tf 12.018 0 0 12.018 278.49 166.05 Tm 0.378 Tc [(CP)-4055(C)-10(P)]TJ /T105 1 Tf 8.386 0 0 8.386 264.09 160.41 Tm 7.561 Tc (\211\211)Tj /F17 1 Tf 12.018 0 0 12.018 303.09 166.05 Tm 0 Tc 0 Tw (v)Tj 18.028 0 0 18.028 243.33 163.29 Tm 2.995 Tc (\234\234)Tj /F11 1 Tf 12 0 0 12 90.09 126.09 Tm -0.001 Tc 0.031 Tw [(Theore)-7(m)12( 8.3:)]TJ /F8 1 Tf 5.74 0 TD 0 Tc 0.04 Tw [( )10(Und)-10(e)4(r the assumption 8.1 if )]TJ /F9 1 Tf 13.03 0 TD 1.39 Tc [(\012[)720(\\)540(\010)1020(\011)30(\020)1433(])]TJ ET q 1 i 342.93 138.09 50.52 -18 re W* n BT /F5 1 Tf 12 0 0 12 342.93 126.09 Tm 1.789 Tc (SS)Tj ET Q BT /F18 1 Tf 12 0 0 12 358.77 126.09 Tm 0 Tc 0 Tw (N)Tj /F17 1 Tf -4.29 0 TD 0.76 Tc [(8\036)-3240(\037)]TJ /F8 1 Tf 8.56 0 TD 0.001 Tc 0.039 Tw [( is not a singleton, it is)]TJ -26.66 -1.67 TD -0.001 Tc 0.001 Tw [(a strongly better response cy)-7(cle.)]TJ ET endstream endobj 205 0 obj << /ProcSet [/PDF /Text /ImageB ] /Font << /F3 38 0 R /F4 43 0 R /F5 46 0 R /F6 47 0 R /F7 48 0 R /F8 49 0 R /F9 50 0 R /F10 61 0 R /F11 62 0 R /F12 90 0 R /F17 206 0 R /F18 207 0 R /T105 201 0 R /T107 208 0 R /T108 209 0 R /T109 210 0 R /T110 211 0 R /T111 212 0 R /T112 213 0 R /T113 214 0 R /T114 215 0 R /T115 216 0 R /T116 217 0 R /T117 218 0 R >> /ExtGState << /GS1 39 0 R >> >> endobj 219 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 64 0 obj << /Name /T10 /Type /Font /Subtype /Type3 /Resources 219 0 R /FontBBox [3 -18 32 53] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 8 /LastChar 92 /Encoding 220 0 R /CharProcs 221 0 R /Widths [27 27 0 0 0 0 0 0 35 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 ] >> endobj 220 0 obj << /Type /Encoding /Differences [8/c8 /c9 16/c16 /c17 92/c92 ] >> endobj 221 0 obj << /c8 222 0 R /c9 223 0 R /c16 224 0 R /c17 225 0 R /c92 226 0 R >> endobj 222 0 obj << /Length 172 >> stream 27 0 6 53 23 -18 d1 q 17 0 0 71 6 -18 cm BI /W 17 /H 71 /BPC 1 /IM true /F /CCF /DP <> ID UJ*ҥRu]W_z~ݿn۶ EI Q endstream endobj 223 0 obj << /Length 171 >> stream 27 0 4 53 21 -18 d1 q 17 0 0 71 4 -18 cm BI /W 17 /H 71 /BPC 1 /IM true /F /CCF /DP <> ID ^ݻ{o۷w_u]W^KҥTF EI Q endstream endobj 224 0 obj << /Length 174 >> stream 35 0 3 47 32 0 d1 q 29 0 0 47 3 0 cm BI /W 29 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID (:'A7IM-i[Xa EI Q endstream endobj 225 0 obj << /Length 157 >> stream 35 0 6 47 29 0 d1 q 23 0 0 47 6 0 cm BI /W 23 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID $u,ME#PQ EI Q endstream endobj 226 0 obj << /Length 148 >> stream 19 0 8 53 11 -18 d1 q 3 0 0 71 8 -18 cm BI /W 3 /H 71 /BPC 1 /IM true /F /CCF /DP <> ID Sj EI Q endstream endobj 227 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 66 0 obj << /Name /T12 /Type /Font /Subtype /Type3 /Resources 227 0 R /FontBBox [6 0 30 44] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 83 /LastChar 84 /Encoding 228 0 R /CharProcs 229 0 R /Widths [29 23 ] >> endobj 228 0 obj << /Type /Encoding /Differences [83/c83 /c84 ] >> endobj 229 0 obj << /c83 230 0 R /c84 231 0 R >> endobj 230 0 obj << /Length 169 >> stream 29 0 6 31 30 0 d1 q 24 0 0 31 6 0 cm BI /W 24 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID !t^8Ay=pnj+o %uJ @ EI Q endstream endobj 231 0 obj << /Length 162 >> stream 23 0 6 44 26 0 d1 q 20 0 0 44 6 0 cm BI /W 20 /H 44 /BPC 1 /IM true /F /CCF /DP <> ID !__Y3ׯׯ/Kb EI Q endstream endobj 232 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 69 0 obj << /Name /T15 /Type /Font /Subtype /Type3 /Resources 232 0 R /FontBBox [6 -3 49 38] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 14 /LastChar 31 /Encoding 233 0 R /CharProcs 234 0 R /Widths [54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54 ] >> endobj 233 0 obj << /Type /Encoding /Differences [14/c14 31/c31 ] >> endobj 234 0 obj << /c14 235 0 R /c31 236 0 R >> endobj 235 0 obj << /Length 131 >> stream 54 0 6 19 48 16 d1 q 42 0 0 3 6 16 cm BI /W 42 /H 3 /BPC 1 /IM true /F /CCF /DP <> ID & EI Q endstream endobj 236 0 obj << /Length 194 >> stream 54 0 6 38 49 -3 d1 q 43 0 0 41 6 -3 cm BI /W 43 /H 41 /BPC 1 /IM true /F /CCF /DP <> ID #8a8appÆpÆ0 (AB (AB P PP @ EI Q endstream endobj 237 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 80 0 obj << /Name /T23 /Type /Font /Subtype /Type3 /Resources 237 0 R /FontBBox [5 0 31 47] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 17 /LastChar 18 /Encoding 238 0 R /CharProcs 239 0 R /Widths [35 35 ] >> endobj 238 0 obj << /Type /Encoding /Differences [17/c17 /c18 ] >> endobj 239 0 obj << /c17 240 0 R /c18 241 0 R >> endobj 240 0 obj << /Length 157 >> stream 35 0 6 47 29 0 d1 q 23 0 0 47 6 0 cm BI /W 23 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID $u,ME#PQ EI Q endstream endobj 241 0 obj << /Length 173 >> stream 35 0 5 47 31 0 d1 q 26 0 0 47 5 0 cm BI /W 26 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID 4:7:0&?M}>ZZKTRTK-%Jt?_ EI Q endstream endobj 242 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 81 0 obj << /Name /T24 /Type /Font /Subtype /Type3 /Resources 242 0 R /FontBBox [-2 -14 45 48] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 42 /LastChar 74 /Encoding 243 0 R /CharProcs 244 0 R /Widths [37 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 ] >> endobj 243 0 obj << /Type /Encoding /Differences [42/c42 74/c74 ] >> endobj 244 0 obj << /c42 245 0 R /c74 246 0 R >> endobj 245 0 obj << /Length 167 >> stream 37 0 7 48 45 0 d1 q 38 0 0 48 7 0 cm BI /W 38 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID )?eu__.uO%IzVҶ ( EI Q endstream endobj 246 0 obj << /Length 179 >> stream 21 0 -2 46 26 -14 d1 q 28 0 0 60 -2 -14 cm BI /W 28 /H 60 /BPC 1 /IM true /F /CCF /DP <> ID !::4: ]/~~~~~u.UB EI Q endstream endobj 247 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 83 0 obj << /Name /T26 /Type /Font /Subtype /Type3 /Resources 247 0 R /FontBBox [5 -18 31 53] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 17 /LastChar 92 /Encoding 248 0 R /CharProcs 249 0 R /Widths [35 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 ] >> endobj 248 0 obj << /Type /Encoding /Differences [17/c17 /c18 92/c92 ] >> endobj 249 0 obj << /c17 250 0 R /c18 251 0 R /c92 252 0 R >> endobj 250 0 obj << /Length 157 >> stream 35 0 6 47 29 0 d1 q 23 0 0 47 6 0 cm BI /W 23 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID $u,ME#PQ EI Q endstream endobj 251 0 obj << /Length 173 >> stream 35 0 5 47 31 0 d1 q 26 0 0 47 5 0 cm BI /W 26 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID 4:7:0&?M}>ZZKTRTK-%Jt?_ EI Q endstream endobj 252 0 obj << /Length 148 >> stream 19 0 8 53 11 -18 d1 q 3 0 0 71 8 -18 cm BI /W 3 /H 71 /BPC 1 /IM true /F /CCF /DP <> ID Sj EI Q endstream endobj 253 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 84 0 obj << /Name /T27 /Type /Font /Subtype /Type3 /Resources 253 0 R /FontBBox [-1 -10 32 34] /FontMatrix [0.02041 0 0 0.02041 0 0] /FirstChar 42 /LastChar 74 /Encoding 254 0 R /CharProcs 255 0 R /Widths [26 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 ] >> endobj 254 0 obj << /Type /Encoding /Differences [42/c42 74/c74 ] >> endobj 255 0 obj << /c42 256 0 R /c74 257 0 R >> endobj 256 0 obj << /Length 156 >> stream 26 0 5 34 32 0 d1 q 27 0 0 34 5 0 cm BI /W 27 /H 34 /BPC 1 /IM true /F /CCF /DP <> ID !cik+ EI Q endstream endobj 257 0 obj << /Length 165 >> stream 15 0 -1 32 18 -10 d1 q 19 0 0 42 -1 -10 cm BI /W 19 /H 42 /BPC 1 /IM true /F /CCF /DP <> ID Z/]}uuuuuuեK @ EI Q endstream endobj 258 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 85 0 obj << /Name /T28 /Type /Font /Subtype /Type3 /Resources 258 0 R /FontBBox [-2 -14 45 48] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 42 /LastChar 83 /Encoding 259 0 R /CharProcs 260 0 R /Widths [37 0 0 0 0 0 0 0 0 39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 32 0 0 0 0 0 0 0 29 ] >> endobj 259 0 obj << /Type /Encoding /Differences [42/c42 51/c51 74/c74 /c75 83/c83 ] >> endobj 260 0 obj << /c42 261 0 R /c51 262 0 R /c74 263 0 R /c75 264 0 R /c83 265 0 R >> endobj 261 0 obj << /Length 167 >> stream 37 0 7 48 45 0 d1 q 38 0 0 48 7 0 cm BI /W 38 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID )?eu__.uO%IzVҶ ( EI Q endstream endobj 262 0 obj << /Length 196 >> stream 39 0 5 48 45 0 d1 q 40 0 0 48 5 0 cm BI /W 40 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID aւuIץ__w\w` [`pynoT]v#j`HP EI Q endstream endobj 263 0 obj << /Length 179 >> stream 21 0 -2 46 26 -14 d1 q 28 0 0 60 -2 -14 cm BI /W 28 /H 60 /BPC 1 /IM true /F /CCF /DP <> ID !::4: ]/~~~~~u.UB EI Q endstream endobj 264 0 obj << /Length 188 >> stream 32 0 6 48 36 0 d1 q 30 0 0 48 6 0 cm BI /W 30 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID ')^Pz ZA}UR-$=*zoz^ӯj EI Q endstream endobj 265 0 obj << /Length 169 >> stream 29 0 6 31 30 0 d1 q 24 0 0 31 6 0 cm BI /W 24 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID !t^8Ay=pnj+o %uJ @ EI Q endstream endobj 266 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 86 0 obj << /Name /T29 /Type /Font /Subtype /Type3 /Resources 266 0 R /FontBBox [4 -3 50 38] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 30 /LastChar 137 /Encoding 267 0 R /CharProcs 268 0 R /Widths [54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 46 ] >> endobj 267 0 obj << /Type /Encoding /Differences [30/c30 118/c118 137/c137 ] >> endobj 268 0 obj << /c30 269 0 R /c118 270 0 R /c137 271 0 R >> endobj 269 0 obj << /Length 138 >> stream 54 0 4 26 50 9 d1 q 46 0 0 17 4 9 cm BI /W 46 /H 17 /BPC 1 /IM true /F /CCF /DP <> ID &7ɨ+x EI Q endstream endobj 270 0 obj << /Length 158 >> stream 54 0 4 33 50 2 d1 q 46 0 0 31 4 2 cm BI /W 46 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID "iRJn*TRJ)5o!TR EI Q endstream endobj 271 0 obj << /Length 173 >> stream 46 0 6 38 41 -3 d1 q 35 0 0 41 6 -3 cm BI /W 35 /H 41 /BPC 1 /IM true /F /CCF /DP <> ID 50nARKU/5o{۷av`@ EI Q endstream endobj 272 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 101 0 obj << /Name /T34 /Type /Font /Subtype /Type3 /Resources 272 0 R /FontBBox [4 0 60 48] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 43 /LastChar 77 /Encoding 273 0 R /CharProcs 274 0 R /Widths [54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 57 ] >> endobj 273 0 obj << /Type /Encoding /Differences [43/c43 77/c77 ] >> endobj 274 0 obj << /c43 275 0 R /c77 276 0 R >> endobj 275 0 obj << /Length 199 >> stream 54 0 4 48 60 0 d1 q 56 0 0 48 4 0 cm BI /W 56 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID $r52-H*KAҪ]-% tJEx^}uouV]4p Ω@ @ EI Q endstream endobj 276 0 obj << /Length 196 >> stream 57 0 6 31 59 0 d1 q 53 0 0 31 6 0 cm BI /W 53 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID 8dH*`/.]h'դ&UzGZRzikUZZ EI Q endstream endobj 277 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 109 0 obj << /Name /T42 /Type /Font /Subtype /Type3 /Resources 277 0 R /FontBBox [3 -3 47 48] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 56 /LastChar 137 /Encoding 278 0 R /CharProcs 279 0 R /Widths [50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47 ] >> endobj 278 0 obj << /Type /Encoding /Differences [56/c56 137/c137 ] >> endobj 279 0 obj << /c56 280 0 R /c137 281 0 R >> endobj 280 0 obj << /Length 192 >> stream 50 0 3 48 47 0 d1 q 44 0 0 48 3 0 cm BI /W 44 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID 5Ds aAMnti~_[KAwk{h @ EI Q endstream endobj 281 0 obj << /Length 173 >> stream 47 0 6 38 41 -3 d1 q 35 0 0 41 6 -3 cm BI /W 35 /H 41 /BPC 1 /IM true /F /CCF /DP <> ID 50nARKU/5o{۷av`@ EI Q endstream endobj 282 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 124 0 obj << /Name /T45 /Type /Font /Subtype /Type3 /Resources 282 0 R /FontBBox [5 0 45 48] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 51 /LastChar 83 /Encoding 283 0 R /CharProcs 284 0 R /Widths [39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29 ] >> endobj 283 0 obj << /Type /Encoding /Differences [51/c51 83/c83 ] >> endobj 284 0 obj << /c51 285 0 R /c83 286 0 R >> endobj 285 0 obj << /Length 196 >> stream 39 0 5 48 45 0 d1 q 40 0 0 48 5 0 cm BI /W 40 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID aւuIץ__w\w` [`pynoT]v#j`HP EI Q endstream endobj 286 0 obj << /Length 169 >> stream 29 0 6 31 30 0 d1 q 24 0 0 31 6 0 cm BI /W 24 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID !t^8Ay=pnj+o %uJ @ EI Q endstream endobj 287 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 148 0 obj << /Name /T56 /Type /Font /Subtype /Type3 /Resources 287 0 R /FontBBox [4 0 58 50] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 33 /LastChar 36 /Encoding 288 0 R /CharProcs 289 0 R /Widths [52 49 50 53 ] >> endobj 288 0 obj << /Type /Encoding /Differences [33/c33 /c34 /c35 /c36 ] >> endobj 289 0 obj << /c33 290 0 R /c34 291 0 R /c35 292 0 R /c36 293 0 R >> endobj 290 0 obj << /Length 178 >> stream 52 0 5 50 49 0 d1 q 44 0 0 50 5 0 cm BI /W 44 /H 50 /BPC 1 /IM true /F /CCF /DP <> ID "]}?_Zu믮]|uVW_O_]/4u EI Q endstream endobj 291 0 obj << /Length 187 >> stream 49 0 4 48 52 0 d1 q 48 0 0 48 4 0 cm BI /W 48 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID $f#izi}t] OPn֩i.%#V EI Q endstream endobj 292 0 obj << /Length 196 >> stream 50 0 11 48 58 0 d1 q 47 0 0 48 11 0 cm BI /W 47 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID * 4 AJo<%T=.K~ V}_m}]-uVҶV҆P(0P EI Q endstream endobj 293 0 obj << /Length 183 >> stream 53 0 4 48 54 0 d1 q 50 0 0 48 4 0 cm BI /W 50 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID $f2nMW~Uu_үuTKT\%P@ @ EI Q endstream endobj 294 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 149 0 obj << /Name /T57 /Type /Font /Subtype /Type3 /Resources 294 0 R /FontBBox [5 0 31 47] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 17 /LastChar 18 /Encoding 295 0 R /CharProcs 296 0 R /Widths [35 35 ] >> endobj 295 0 obj << /Type /Encoding /Differences [17/c17 /c18 ] >> endobj 296 0 obj << /c17 297 0 R /c18 298 0 R >> endobj 297 0 obj << /Length 157 >> stream 35 0 6 47 29 0 d1 q 23 0 0 47 6 0 cm BI /W 23 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID $u,ME#PQ EI Q endstream endobj 298 0 obj << /Length 173 >> stream 35 0 5 47 31 0 d1 q 26 0 0 47 5 0 cm BI /W 26 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID 4:7:0&?M}>ZZKTRTK-%Jt?_ EI Q endstream endobj 299 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 151 0 obj << /Name /T59 /Type /Font /Subtype /Type3 /Resources 299 0 R /FontBBox [4 -14 37 31] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 88 /LastChar 90 /Encoding 300 0 R /CharProcs 301 0 R /Widths [32 34 29 ] >> endobj 300 0 obj << /Type /Encoding /Differences [88/c88 /c89 /c90 ] >> endobj 301 0 obj << /c88 302 0 R /c89 303 0 R /c90 304 0 R >> endobj 302 0 obj << /Length 181 >> stream 32 0 4 31 37 0 d1 q 33 0 0 31 4 0 cm BI /W 33 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID (32tkh'JҍRZ}p,}zz}uS#KKBb EI Q endstream endobj 303 0 obj << /Length 189 >> stream 34 0 6 31 36 -14 d1 q 30 0 0 45 6 -14 cm BI /W 30 /H 45 /BPC 1 /IM true /F /CCF /DP <> ID >ά h _Wkֿ}봬|4YKKIi+P EI Q endstream endobj 304 0 obj << /Length 175 >> stream 29 0 4 31 33 0 d1 q 29 0 0 31 4 0 cm BI /W 29 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID $PT֝QxcTJ*TBTRHR]$Fu@v+ L* EI Q endstream endobj 305 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 152 0 obj << /Name /T60 /Type /Font /Subtype /Type3 /Resources 305 0 R /FontBBox [4 -14 37 31] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 88 /LastChar 90 /Encoding 306 0 R /CharProcs 307 0 R /Widths [32 34 29 ] >> endobj 306 0 obj << /Type /Encoding /Differences [88/c88 /c89 /c90 ] >> endobj 307 0 obj << /c88 308 0 R /c89 309 0 R /c90 310 0 R >> endobj 308 0 obj << /Length 181 >> stream 32 0 4 31 37 0 d1 q 33 0 0 31 4 0 cm BI /W 33 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID (32tkh'JҍRZ}p,}zz}uS#KKBb EI Q endstream endobj 309 0 obj << /Length 189 >> stream 34 0 6 31 36 -14 d1 q 30 0 0 45 6 -14 cm BI /W 30 /H 45 /BPC 1 /IM true /F /CCF /DP <> ID >ά h _Wkֿ}봬|4YKKIi+P EI Q endstream endobj 310 0 obj << /Length 175 >> stream 29 0 4 31 33 0 d1 q 29 0 0 31 4 0 cm BI /W 29 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID $PT֝QxcTJ*TBTRHR]$Fu@v+ L* EI Q endstream endobj 311 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 153 0 obj << /Name /T61 /Type /Font /Subtype /Type3 /Resources 311 0 R /FontBBox [4 0 54 48] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 34 /LastChar 90 /Encoding 312 0 R /CharProcs 313 0 R /Widths [49 0 53 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29 ] >> endobj 312 0 obj << /Type /Encoding /Differences [34/c34 36/c36 90/c90 ] >> endobj 313 0 obj << /c34 314 0 R /c36 315 0 R /c90 316 0 R >> endobj 314 0 obj << /Length 187 >> stream 49 0 4 48 52 0 d1 q 48 0 0 48 4 0 cm BI /W 48 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID $f#izi}t] OPn֩i.%#V EI Q endstream endobj 315 0 obj << /Length 183 >> stream 53 0 4 48 54 0 d1 q 50 0 0 48 4 0 cm BI /W 50 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID $f2nMW~Uu_үuTKT\%P@ @ EI Q endstream endobj 316 0 obj << /Length 175 >> stream 29 0 4 31 33 0 d1 q 29 0 0 31 4 0 cm BI /W 29 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID $PT֝QxcTJ*TBTRHR]$Fu@v+ L* EI Q endstream endobj 317 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 154 0 obj << /Name /T62 /Type /Font /Subtype /Type3 /Resources 317 0 R /FontBBox [4 -14 54 50] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 33 /LastChar 89 /Encoding 318 0 R /CharProcs 319 0 R /Widths [52 0 0 53 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 34 ] >> endobj 318 0 obj << /Type /Encoding /Differences [33/c33 36/c36 88/c88 /c89 ] >> endobj 319 0 obj << /c33 320 0 R /c36 321 0 R /c88 322 0 R /c89 323 0 R >> endobj 320 0 obj << /Length 178 >> stream 52 0 5 50 49 0 d1 q 44 0 0 50 5 0 cm BI /W 44 /H 50 /BPC 1 /IM true /F /CCF /DP <> ID "]}?_Zu믮]|uVW_O_]/4u EI Q endstream endobj 321 0 obj << /Length 183 >> stream 53 0 4 48 54 0 d1 q 50 0 0 48 4 0 cm BI /W 50 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID $f2nMW~Uu_үuTKT\%P@ @ EI Q endstream endobj 322 0 obj << /Length 181 >> stream 32 0 4 31 37 0 d1 q 33 0 0 31 4 0 cm BI /W 33 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID (32tkh'JҍRZ}p,}zz}uS#KKBb EI Q endstream endobj 323 0 obj << /Length 189 >> stream 34 0 6 31 36 -14 d1 q 30 0 0 45 6 -14 cm BI /W 30 /H 45 /BPC 1 /IM true /F /CCF /DP <> ID >ά h _Wkֿ}봬|4YKKIi+P EI Q endstream endobj 324 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 159 0 obj << /Name /T67 /Type /Font /Subtype /Type3 /Resources 324 0 R /FontBBox [4 0 60 48] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 43 /LastChar 90 /Encoding 325 0 R /CharProcs 326 0 R /Widths [54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 32 0 57 0 0 0 0 0 0 0 0 0 0 0 0 29 ] >> endobj 325 0 obj << /Type /Encoding /Differences [43/c43 58/c58 75/c75 77/c77 90/c90 ] >> endobj 326 0 obj << /c43 327 0 R /c58 328 0 R /c75 329 0 R /c77 330 0 R /c90 331 0 R >> endobj 327 0 obj << /Length 199 >> stream 54 0 4 48 60 0 d1 q 56 0 0 48 4 0 cm BI /W 56 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID $r52-H*KAҪ]-% tJEx^}uouV]4p Ω@ @ EI Q endstream endobj 328 0 obj << /Length 185 >> stream 43 0 5 48 49 0 d1 q 44 0 0 48 5 0 cm BI /W 44 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID :FZZU$ꪖt,j*TTRR:UKKTJi @ EI Q endstream endobj 329 0 obj << /Length 188 >> stream 32 0 6 48 36 0 d1 q 30 0 0 48 6 0 cm BI /W 30 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID ')^Pz ZA}UR-$=*zoz^ӯj EI Q endstream endobj 330 0 obj << /Length 196 >> stream 57 0 6 31 59 0 d1 q 53 0 0 31 6 0 cm BI /W 53 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID 8dH*`/.]h'դ&UzGZRzikUZZ EI Q endstream endobj 331 0 obj << /Length 175 >> stream 29 0 4 31 33 0 d1 q 29 0 0 31 4 0 cm BI /W 29 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID $PT֝QxcTJ*TBTRHR]$Fu@v+ L* EI Q endstream endobj 332 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 161 0 obj << /Name /T69 /Type /Font /Subtype /Type3 /Resources 332 0 R /FontBBox [3 0 32 47] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 16 /LastChar 18 /Encoding 333 0 R /CharProcs 334 0 R /Widths [35 0 35 ] >> endobj 333 0 obj << /Type /Encoding /Differences [16/c16 18/c18 ] >> endobj 334 0 obj << /c16 335 0 R /c18 336 0 R >> endobj 335 0 obj << /Length 174 >> stream 35 0 3 47 32 0 d1 q 29 0 0 47 3 0 cm BI /W 29 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID (:'A7IM-i[Xa EI Q endstream endobj 336 0 obj << /Length 173 >> stream 35 0 5 47 31 0 d1 q 26 0 0 47 5 0 cm BI /W 26 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID 4:7:0&?M}>ZZKTRTK-%Jt?_ EI Q endstream endobj 337 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 163 0 obj << /Name /T71 /Type /Font /Subtype /Type3 /Resources 337 0 R /FontBBox [1 0 33 47] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 16 /LastChar 20 /Encoding 338 0 R /CharProcs 339 0 R /Widths [35 35 0 0 35 ] >> endobj 338 0 obj << /Type /Encoding /Differences [16/c16 /c17 20/c20 ] >> endobj 339 0 obj << /c16 340 0 R /c17 341 0 R /c20 342 0 R >> endobj 340 0 obj << /Length 174 >> stream 35 0 3 47 32 0 d1 q 29 0 0 47 3 0 cm BI /W 29 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID (:'A7IM-i[Xa EI Q endstream endobj 341 0 obj << /Length 157 >> stream 35 0 6 47 29 0 d1 q 23 0 0 47 6 0 cm BI /W 23 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID $u,ME#PQ EI Q endstream endobj 342 0 obj << /Length 170 >> stream 35 0 1 47 33 0 d1 q 32 0 0 47 1 0 cm BI /W 32 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID ֹK_].]}uz_@h EI Q endstream endobj 343 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 167 0 obj << /Name /T73 /Type /Font /Subtype /Type3 /Resources 343 0 R /FontBBox [5 0 31 46] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 17 /LastChar 18 /Encoding 344 0 R /CharProcs 345 0 R /Widths [35 35 ] >> endobj 344 0 obj << /Type /Encoding /Differences [17/c17 /c18 ] >> endobj 345 0 obj << /c17 346 0 R /c18 347 0 R >> endobj 346 0 obj << /Length 155 >> stream 35 0 6 45 29 0 d1 q 23 0 0 45 6 0 cm BI /W 23 /H 45 /BPC 1 /IM true /F /CCF /DP <> ID (QHɨ( @ EI Q endstream endobj 347 0 obj << /Length 173 >> stream 35 0 5 46 31 0 d1 q 26 0 0 46 5 0 cm BI /W 26 /H 46 /BPC 1 /IM true /F /CCF /DP <> ID 4:7:0&=oM}:ץjJ-RR*| @ EI Q endstream endobj 348 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 170 0 obj << /Name /T76 /Type /Font /Subtype /Type3 /Resources 348 0 R /FontBBox [4 0 37 31] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 88 /LastChar 90 /Encoding 349 0 R /CharProcs 350 0 R /Widths [32 0 28 ] >> endobj 349 0 obj << /Type /Encoding /Differences [88/c88 90/c90 ] >> endobj 350 0 obj << /c88 351 0 R /c90 352 0 R >> endobj 351 0 obj << /Length 177 >> stream 32 0 4 31 37 0 d1 q 33 0 0 31 4 0 cm BI /W 33 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID (33AcbүJiq_^OR]*%a+CA EI Q endstream endobj 352 0 obj << /Length 174 >> stream 28 0 4 31 32 0 d1 q 28 0 0 31 4 0 cm BI /W 28 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID $0=4] V+O*TRJ*T]%TΨJ5IV @ EI Q endstream endobj 353 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 172 0 obj << /Name /T78 /Type /Font /Subtype /Type3 /Resources 353 0 R /FontBBox [4 0 52 50] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 33 /LastChar 34 /Encoding 354 0 R /CharProcs 355 0 R /Widths [52 49 ] >> endobj 354 0 obj << /Type /Encoding /Differences [33/c33 /c34 ] >> endobj 355 0 obj << /c33 356 0 R /c34 357 0 R >> endobj 356 0 obj << /Length 178 >> stream 52 0 5 50 49 0 d1 q 44 0 0 50 5 0 cm BI /W 44 /H 50 /BPC 1 /IM true /F /CCF /DP <> ID "]}?_Zu믮]|uVW_O_]/4u EI Q endstream endobj 357 0 obj << /Length 187 >> stream 49 0 4 48 52 0 d1 q 48 0 0 48 4 0 cm BI /W 48 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID $f#izi}t] OPn֩i.%#V EI Q endstream endobj 358 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 173 0 obj << /Name /T79 /Type /Font /Subtype /Type3 /Resources 358 0 R /FontBBox [4 0 58 48] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 35 /LastChar 36 /Encoding 359 0 R /CharProcs 360 0 R /Widths [50 53 ] >> endobj 359 0 obj << /Type /Encoding /Differences [35/c35 /c36 ] >> endobj 360 0 obj << /c35 361 0 R /c36 362 0 R >> endobj 361 0 obj << /Length 196 >> stream 50 0 11 48 58 0 d1 q 47 0 0 48 11 0 cm BI /W 47 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID * 4 AJo<%T=.K~ V}_m}]-uVҶV҆P(0P EI Q endstream endobj 362 0 obj << /Length 183 >> stream 53 0 4 48 54 0 d1 q 50 0 0 48 4 0 cm BI /W 50 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID $f2nMW~Uu_үuTKT\%P@ @ EI Q endstream endobj 363 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 177 0 obj << /Name /T83 /Type /Font /Subtype /Type3 /Resources 363 0 R /FontBBox [3 0 32 47] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 16 /LastChar 18 /Encoding 364 0 R /CharProcs 365 0 R /Widths [35 0 35 ] >> endobj 364 0 obj << /Type /Encoding /Differences [16/c16 18/c18 ] >> endobj 365 0 obj << /c16 366 0 R /c18 367 0 R >> endobj 366 0 obj << /Length 174 >> stream 35 0 3 47 32 0 d1 q 29 0 0 47 3 0 cm BI /W 29 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID (:'A7IM-i[Xa EI Q endstream endobj 367 0 obj << /Length 173 >> stream 35 0 5 47 31 0 d1 q 26 0 0 47 5 0 cm BI /W 26 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID 4:7:0&?M}>ZZKTRTK-%Jt?_ EI Q endstream endobj 368 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 185 0 obj << /Name /T91 /Type /Font /Subtype /Type3 /Resources 368 0 R /FontBBox [-2 -14 60 48] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 43 /LastChar 75 /Encoding 369 0 R /CharProcs 370 0 R /Widths [54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 21 32 ] >> endobj 369 0 obj << /Type /Encoding /Differences [43/c43 74/c74 /c75 ] >> endobj 370 0 obj << /c43 371 0 R /c74 372 0 R /c75 373 0 R >> endobj 371 0 obj << /Length 199 >> stream 54 0 4 48 60 0 d1 q 56 0 0 48 4 0 cm BI /W 56 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID $r52-H*KAҪ]-% tJEx^}uouV]4p Ω@ @ EI Q endstream endobj 372 0 obj << /Length 179 >> stream 21 0 -2 46 26 -14 d1 q 28 0 0 60 -2 -14 cm BI /W 28 /H 60 /BPC 1 /IM true /F /CCF /DP <> ID !::4: ]/~~~~~u.UB EI Q endstream endobj 373 0 obj << /Length 188 >> stream 32 0 6 48 36 0 d1 q 30 0 0 48 6 0 cm BI /W 30 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID ')^Pz ZA}UR-$=*zoz^ӯj EI Q endstream endobj 374 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 186 0 obj << /Name /T92 /Type /Font /Subtype /Type3 /Resources 374 0 R /FontBBox [4 -6 51 41] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 12 /LastChar 30 /Encoding 375 0 R /CharProcs 376 0 R /Widths [54 0 54 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 54 ] >> endobj 375 0 obj << /Type /Encoding /Differences [12/c12 14/c14 30/c30 ] >> endobj 376 0 obj << /c12 377 0 R /c14 378 0 R /c30 379 0 R >> endobj 377 0 obj << /Length 153 >> stream 54 0 4 41 51 -6 d1 q 47 0 0 47 4 -6 cm BI /W 47 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID 8*jA EI Q endstream endobj 378 0 obj << /Length 131 >> stream 54 0 6 19 48 16 d1 q 42 0 0 3 6 16 cm BI /W 42 /H 3 /BPC 1 /IM true /F /CCF /DP <> ID & EI Q endstream endobj 379 0 obj << /Length 138 >> stream 54 0 4 26 50 9 d1 q 46 0 0 17 4 9 cm BI /W 46 /H 17 /BPC 1 /IM true /F /CCF /DP <> ID &7ɨ+x EI Q endstream endobj 380 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 191 0 obj << /Name /T95 /Type /Font /Subtype /Type3 /Resources 380 0 R /FontBBox [3 0 32 47] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 16 /LastChar 17 /Encoding 381 0 R /CharProcs 382 0 R /Widths [35 35 ] >> endobj 381 0 obj << /Type /Encoding /Differences [16/c16 /c17 ] >> endobj 382 0 obj << /c16 383 0 R /c17 384 0 R >> endobj 383 0 obj << /Length 174 >> stream 35 0 3 47 32 0 d1 q 29 0 0 47 3 0 cm BI /W 29 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID (:'A7IM-i[Xa EI Q endstream endobj 384 0 obj << /Length 157 >> stream 35 0 6 47 29 0 d1 q 23 0 0 47 6 0 cm BI /W 23 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID $u,ME#PQ EI Q endstream endobj 385 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 193 0 obj << /Name /T97 /Type /Font /Subtype /Type3 /Resources 385 0 R /FontBBox [4 -18 23 53] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 8 /LastChar 9 /Encoding 386 0 R /CharProcs 387 0 R /Widths [27 27 ] >> endobj 386 0 obj << /Type /Encoding /Differences [8/c8 /c9 ] >> endobj 387 0 obj << /c8 388 0 R /c9 389 0 R >> endobj 388 0 obj << /Length 172 >> stream 27 0 6 53 23 -18 d1 q 17 0 0 71 6 -18 cm BI /W 17 /H 71 /BPC 1 /IM true /F /CCF /DP <> ID UJ*ҥRu]W_z~ݿn۶ EI Q endstream endobj 389 0 obj << /Length 171 >> stream 27 0 4 53 21 -18 d1 q 17 0 0 71 4 -18 cm BI /W 17 /H 71 /BPC 1 /IM true /F /CCF /DP <> ID ^ݻ{o۷w_u]W^KҥTF EI Q endstream endobj 390 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 194 0 obj << /Name /T98 /Type /Font /Subtype /Type3 /Resources 390 0 R /FontBBox [6 0 57 47] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 52 /LastChar 83 /Encoding 391 0 R /CharProcs 392 0 R /Widths [50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29 ] >> endobj 391 0 obj << /Type /Encoding /Differences [52/c52 83/c83 ] >> endobj 392 0 obj << /c52 393 0 R /c83 394 0 R >> endobj 393 0 obj << /Length 173 >> stream 50 0 12 47 57 0 d1 q 45 0 0 47 12 0 cm BI /W 45 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID 8$rH[oJk]ur8 @ EI Q endstream endobj 394 0 obj << /Length 169 >> stream 29 0 6 31 30 0 d1 q 24 0 0 31 6 0 cm BI /W 24 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID !t^8Ay=pnj+o %uJ @ EI Q endstream endobj 395 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 199 0 obj << /Name /T103 /Type /Font /Subtype /Type3 /Resources 395 0 R /FontBBox [4 0 67 30] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 100 /LastChar 108 /Encoding 396 0 R /CharProcs 397 0 R /Widths [70 0 0 0 0 0 0 0 70 ] >> endobj 396 0 obj << /Type /Encoding /Differences [100/c100 108/c108 ] >> endobj 397 0 obj << /c100 398 0 R /c108 399 0 R >> endobj 398 0 obj << /Length 213 >> stream 70 0 4 30 66 0 d1 q 62 0 0 30 4 0 cm BI /W 62 /H 30 /BPC 1 /IM true /F /CCF /DP <> ID '08 `AAeZ i7M鴾mnoju6z0Mt YZJ΄ P` EI Q endstream endobj 399 0 obj << /Length 151 >> stream 70 0 4 30 67 5 d1 q 63 0 0 25 4 5 cm BI /W 63 /H 25 /BPC 1 /IM true /F /CCF /DP <> ID *_nݻv9)ڕARJ-W^ EI Q endstream endobj 400 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 200 0 obj << /Name /T104 /Type /Font /Subtype /Type3 /Resources 400 0 R /FontBBox [5 0 45 48] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 51 /LastChar 83 /Encoding 401 0 R /CharProcs 402 0 R /Widths [39 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29 ] >> endobj 401 0 obj << /Type /Encoding /Differences [51/c51 83/c83 ] >> endobj 402 0 obj << /c51 403 0 R /c83 404 0 R >> endobj 403 0 obj << /Length 196 >> stream 39 0 5 48 45 0 d1 q 40 0 0 48 5 0 cm BI /W 40 /H 48 /BPC 1 /IM true /F /CCF /DP <> ID aւuIץ__w\w` [`pynoT]v#j`HP EI Q endstream endobj 404 0 obj << /Length 169 >> stream 29 0 6 31 30 0 d1 q 24 0 0 31 6 0 cm BI /W 24 /H 31 /BPC 1 /IM true /F /CCF /DP <> ID !t^8Ay=pnj+o %uJ @ EI Q endstream endobj 405 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 208 0 obj << /Name /T107 /Type /Font /Subtype /Type3 /Resources 405 0 R /FontBBox [3 0 32 47] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 16 /LastChar 17 /Encoding 406 0 R /CharProcs 407 0 R /Widths [35 35 ] >> endobj 406 0 obj << /Type /Encoding /Differences [16/c16 /c17 ] >> endobj 407 0 obj << /c16 408 0 R /c17 409 0 R >> endobj 408 0 obj << /Length 174 >> stream 35 0 3 47 32 0 d1 q 29 0 0 47 3 0 cm BI /W 29 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID (:'A7IM-i[Xa EI Q endstream endobj 409 0 obj << /Length 157 >> stream 35 0 6 47 29 0 d1 q 23 0 0 47 6 0 cm BI /W 23 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID $u,ME#PQ EI Q endstream endobj 410 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 216 0 obj << /Name /T115 /Type /Font /Subtype /Type3 /Resources 410 0 R /FontBBox [5 0 31 47] /FontMatrix [0.01449 0 0 0.01449 0 0] /FirstChar 17 /LastChar 18 /Encoding 411 0 R /CharProcs 412 0 R /Widths [35 35 ] >> endobj 411 0 obj << /Type /Encoding /Differences [17/c17 /c18 ] >> endobj 412 0 obj << /c17 413 0 R /c18 414 0 R >> endobj 413 0 obj << /Length 157 >> stream 35 0 6 47 29 0 d1 q 23 0 0 47 6 0 cm BI /W 23 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID $u,ME#PQ EI Q endstream endobj 414 0 obj << /Length 173 >> stream 35 0 5 47 31 0 d1 q 26 0 0 47 5 0 cm BI /W 26 /H 47 /BPC 1 /IM true /F /CCF /DP <> ID 4:7:0&?M}>ZZKTRTK-%Jt?_ EI Q endstream endobj 415 0 obj << /ProcSet [/PDF /ImageB ] >> endobj 217 0 obj << /Name /T116 /Type /Font /Subtype /Type3 /Resources 415 0 R /FontBBox [4 -1 23 34] /FontMatrix [0.02 0 0 0.02 0 0] /FirstChar 17 /LastChar 18 /Encoding 416 0 R /CharProcs 417 0 R /Widths [25 25 ] >> endobj 416 0 obj << /Type /Encoding /Differences [17/c17 /c18 ] >> endobj 417 0 obj << /c17 418 0 R /c18 419 0 R >> endobj 418 0 obj << /Length 152 >> stream 25 0 4 33 21 -1 d1 q 17 0 0 34 4 -1 cm BI /W 17 /H 34 /BPC 1 /IM true /F /CCF /DP <> ID 4ad.\cr8/1 EI Q endstream endobj 419 0 obj << /Length 162 >> stream 25 0 4 34 23 0 d1 q 19 0 0 34 4 0 cm BI /W 19 /H 34 /BPC 1 /IM true /F /CCF /DP <> ID