%PDF-1.2 % 22 0 obj << /Length 2771 >> stream BT /F1 1 Tf 18 0 0 18 147.33 587.01 Tm 0 g /GS1 gs 0 Tc 0.002 Tw [(The Nash Threat)26(s Folk Theorem W)4(i)5(th)]TJ -1.4667 -1.1067 TD [(Communication and)4( )27(A)22(pproximate Common)]TJ 2.3067 -1.1133 TD [(Kno)11(w)-22(l)5(e)3(dge )7(in T)91(w)-22(o)4( )7(Play)9(er Games)]TJ 11.52 0 0 11.52 443.25 555.57 Tm 0 Tw (1)Tj /F2 1 Tf 12 0 0 12 265.65 464.01 Tm -0.002 Tc 0.012 Tw [(Drew F)4(udenb)-12(er)-9(g)]TJ -0.15 -1.66 TD 0 Tc 0 Tw [(David K. )-10(L)11(e)4(vine)]TJ 8.04 0 0 8.04 344.13 449.61 Tm (2)Tj 12 0 0 12 237.93 404.01 Tm [(F)6(i)-2(rst Version: Ma)-16(y)20( 24, 2002)]TJ -0.23 -1.66 TD [(This Version: J)-11(une 17, 2004*)]TJ -12.09 -17.82 TD ( )Tj ET 1 i 90.09 173.37 143.88 -0.48 re f BT 8.04 0 0 8.04 90.09 161.01 Tm (1)Tj 12 0 0 12 94.17 155.49 Tm ( )Tj 9.96 0 0 9.96 99.81 155.49 Tm 0.002 Tc 0.266 Tw [(W)-6(e)0( are g)8(r)-2(atef)10(u)8(l)3( to se)-12(m)9(i)-9(n)8(a)0(r participan)8(ts at th)8(e C)6(o)-16(w)13(l)3(e)-12(s)5( )-12(C)6(onf)10(ere)-12(n)8(ce )-12(on)8( )-12(repeated )-12(g)8(a)-12(m)21(e)0( )-24(w)13(i)3(t)-9(h)8( )-12(priv)8(ate)]TJ -0.9759 -1.2048 TD 0 Tc 0.087 Tw [(in)-6(f)8(o)-6(r)-16(m)19(atio)-6(n )-12(w)11(h)-6(o)-6(s)3(e researc)-14(h)6( insp)-18(ired)-6( this p)-6(r)-4(o)-6(j)-11(ect, to)-6( Ichiro)-6( Obara )-12(f)8(o)-6(r )-12(help)-6(f)8(u)6(l )-12(d)-6(i)1(sc)-14(us)-9(sio)-6(n)6(, )-12(a)-14(n)6(d)-6( )-12(to)-6( )-12(the )-12(ed)-6(ito)-6(r)]TJ 0 -1.1566 TD 0.002 Tc 0.134 Tw [(an)8(d associate editor f)10(o)-4(r u)8(s)5(e)-12(f)-2(u)8(l)3( co)-16(m)9(m)9(e)-12(n)8(t)3(s on)8( a)-12(n)8( earlier draf)10(t. )-12(T)-14(h)8(e )-12(associate )-12(editor )-12(an)8(d )-12(Satoru)8( )-12(T)-14(a)0(k)8(a)0(h)8(a)0(shi)]TJ T* -0.005 Tc 0.044 Tw [(he)-7(lp)-11(e)-7(d)-11( us )-12(find)-11( a)-19(n)1( e)-7(r)-9(r)-9(o)-11(r)-9( in the)-7( ma)-19(in p)-11(r)-9(o)-11(o)-11(f)3(; T)-21(a)-7(ka)-7(ha)-7(s)-14(h)1(i a)-19(n)1(d)-11( D)-6(a)-7(m H)-6(o)-11(j)-28(m)14(a)-7(n)1( )-12(he)-7(lp)-11(e)-7(d)-11( p)-11(r)-9(o)-11(o)-11(f-r)-9(e)-7(a)-7(d)-11( va)-7(r)-9(i)-4(o)-11(u)1(s )-12(ve)-7(r)-9(s)-2(io)-11(n)-11(s)-2(.)]TJ T* 0.005 Tc 0.046 Tw [(We are h)11(a)3(ppy)23( t)6(o)-1( ackn)11(o)-13(w)16(l)6(edg)11(e)3( th)11(e s)8(u)11(pport)6( of)13( Nat)6(i)6(o)-1(n)11(a)3(l)6( )-12(S)7(c)3(i)6(e)3(n)11(ce )-12(F)7(oun)11(dat)6(i)6(o)-1(n)11( Gran)11(ts)8( )-12(S)7(E)2(S)7(99-)13(86170 )-12(an)11(d )-12(S)7(E)2(S)7(-)]TJ 0 -1.1446 TD [(0112)12(018.)]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(,)1( Harv)10(ard Uni)5(v)10(ersi)5(ty)22( a)-10(n)10(d UCLA)15(.)]TJ ET endstream endobj 23 0 obj << /ProcSet [/PDF /Text ] /Font << /F1 24 0 R /F2 25 0 R >> /ExtGState << /GS1 26 0 R >> >> endobj 28 0 obj << /Length 7795 >> stream BT /F2 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g /GS1 gs 0 Tc 0 Tw (1)Tj /F1 1 Tf -17.75 -4 TD 0.382 Tw [(1. Introduction)]TJ /F3 1 Tf 3 -1.91 TD -0.001 Tc 0.121 Tw [( )110(I)22(n)-1( )-10(repe)-7(ated )-10(g)9(a)3(m)-13(e)3(s with private monitoring)9(, th)-11(e play)9(e)-7(r)2(s)-12(\222)2( beliefs )-10(about past pla)-17(y)]TJ -3 -1.67 TD 0 Tc 0.18 Tw [(will )10(g)10(r)3(adu)-10(a)4(ll)-12(y)20( )10(d)-10(r)3(ift )10(apart )10(as )10(the g)10(a)4(me g)10(o)-10(es )10(on, which mak)-10(e)4(s it difficult to sustain an)]TJ T* -0.001 Tc 0.111 Tw [(equilibrium )10(that )10(is )10(based on common beliefs. One w)-9(a)-17(y)19( to restor)-8(e common belief )-10(about)]TJ 0 -1.66 TD -0.002 Tc 0.172 Tw [(t)-4(h)-2(e )10(aspect)-4(s )10(of )10(p)-12(a)2(st)-4( pl)-4(a)-18(y)18( t)-4(h)-2(at)-4( m)-4(a)2(t)-4(t)-4(e)2(r fo)-12(r for)-9(ecast)-4(s)-3( of f)-9(u)-2(t)-4(u)-2(re pl)-4(a)-18(y)18( i)-4(s)-3( fo)-12(r pl)-4(a)-18(y)18(ers t)-4(o)-2( send)]TJ 0 -1.67 TD 0.001 Tc 0.139 Tw [(\223)5(c)5(h)1(ea)5(p-ta)5(lk\224)5( me)5(ss)-10(ag)11(e)5(s)0( to one)5( )-10(a)5(nothe)5(r; if the)5(s)0(e)5( m)-11(e)5(ssag)11(e)5(s are)5( truthful, the)-15(y)21( )-20(will )-10(form )-10(a)]TJ T* -0.001 Tc 0.061 Tw [(public state that can be us)-12(ed to g)9(o)-11(vern the pl)-13(a)-17(y)19(ers\222 str)-8(a)3(te)-7(g)9(i)-3(es. Ho)-11(weve)-7(r, one of th)-11(e first)]TJ 0 -1.66 TD 0 Tc 0.08 Tw [(results )10(on using)10( communication in this wa)-16(y)20( is ne)-6(g)10(a)4(tive: Matsushima [)-7(1991])-7( proved that)]TJ 0 -1.67 TD 0.001 Tc 0.129 Tw [(pay)21(o)-9(ffs )10(of e)5(quilibria)5( with truthful, inc)5(e)5(n)1(tive)5( c)5(o)1(mpa)5(tible)5( re)5(ve)5(la)5(tion of the)5( si)-11(g)11(n)-9(a)5(l)-1(s e)5(v)1(e)5(r)-16(y)]TJ T* -0.001 Tc 0.061 Tw [(period )10(ar)-8(e )10(bounded )10(a)-7(w)1(a)-17(y)19( f)-8(r)2(om effi)-13(cienc)-17(y)19( in two-pla)-17(y)19(e)-7(r)2( )-10(games with independent si)-13(g)9(n)-1(als.)]TJ 0 -1.66 TD 0 Tc 0.35 Tw [(Subsequentl)-12(y)20(, )10(Compte )10([)-7(1998])-7( and Kandori and Matsushima [)-7(1998])-7( proved a folk)]TJ 0 -1.67 TD 0.16 Tw [(the)4(o)0(re)4(m )10(for )10(two)-10(-)3(pla)-16(y)20(e)4(r)3( g)10(a)-6(me)4(s )10(with )10(inde)4(pe)4(nd)-10(e)4(n)0(t )10(sig)10(n)-10(a)4(l)-2(s, b)-10(y)20( )-10(c)4(onside)4(r)3(in)-10(g)10( stra)4(teg)10(i)-12(e)4(s)-1( tha)4(t)]TJ T* -0.001 Tc 0.011 Tw [(onl)-13(y)19( repo)-11(rt truthfull)-13(y)19( )-10(ever)-18(y)19( )]TJ /F4 1 Tf 11.19 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 0.56 0 TD -0.001 Tc 0.011 Tw [( pe)-7(riods, wher)-8(e )]TJ /F4 1 Tf 6.42 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 0.56 0 TD -0.001 Tc 0.011 Tw [( g)9(o)-11(es to infinit)-13(y)19( as the )-10(dis)-12(c)3(ount )-10(facto)-11(r)2( )-20(g)9(o)-1(es)]TJ -18.73 -1.66 TD 0 Tc 0 Tw (to 1.)Tj /F2 1 Tf 8.04 0 0 8.04 111.45 434.61 Tm (3)Tj /F3 1 Tf 12 0 0 12 126.09 409.05 Tm 0.12 Tw [(This )10(paper )10(shows )10(how communication )10(can )-10(y)20(i)-2(eld a N)-8(a)4(sh-thr)-7(eats folk theor)-7(e)4(m in)]TJ -3 -1.67 TD 0.19 Tw [(two-pla)-6(y)20(e)-6(r)3( )-10(games with \223almost public\224 information but without independent )-10(si)-12(g)10(n)0(als.)]TJ /F2 1 Tf 8.04 0 0 8.04 518.01 394.53 Tm 0 Tw (4)Tj /F3 1 Tf 12 0 0 12 90.09 369.09 Tm -0.001 Tc 0.071 Tw [(Our proof is a )-10(combination of the idea that )-10(communication provides )-10(a )-10(public )-10(si)-13(g)9(n)-1(al )-10(and)]TJ T* 0 Tc 0.21 Tw [(an idea f)-7(r)3(om Mailath and Morris [)-7(2002])-7(. 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This)]TJ 0 -3.17 TD 0 Tw ( )Tj ET 1 i 90.09 194.13 143.88 -0.48 re f BT /F2 1 Tf 6.48 0 0 6.48 90.09 182.49 Tm (3)Tj 9.96 0 0 9.96 93.33 177.93 Tm 0.003 Tc 0.12 Tw [( )12(In)9( addition)9(,)0( th)9(es)6(e papers)6(, an)9(d als)6(o)-3( B)-5(e)1(n)9(-)11(P)-7(o)-3(rath)9( an)9(d Ka)-11(h)9(n)9(e)-11(m)10(a)1(n [1996], )12(prov)9(ed f)11(o)-3(lk)9( th)9(eore)-11(m)22(s)6( )-13(f)11(o)-3(r g)9(a)-11(m)10(e)1(s)]TJ -0.3253 -1.1446 TD 0.025 Tw [(w)13(i)3(t)-9(h)8( at lea)-12(s)5(t th)8(ree pla)-12(y)20(er)-14(s. 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A)14(o)-15(y)21(a)-11(g)9(i)4( )12([2002] )25(prov)9(es)6( )12(a f)11(o)-3(lk)9( th)9(eore)-11(m)22( )-12(f)11(o)-3(r g)9(a)-11(m)10(e)1(s)6( )-12(w)14(i)-8(th)9( a t)-8(h)9(ird-)11(part)-8(y)21( )-12(m)10(e)1(diator )-12(w)26(ho receiv)9(e)-11(s)]TJ 0 -1.1446 TD 0.073 Tw [(priv)8(ate reports f)10(r)-2(om)21( t)-9(h)8(e pla)-12(y)20(ers a)-12(n)8(d se)-12(n)8(d)-4(s th)8(e)-12(m)9( )-12(n)8(on-)10(bin)8(d)-4(i)-9(n)-4(g)8( instru)8(ct)-9(ion)8(s)5(, as i)-9(n)8( t)-9(h)8(e co)-16(m)9(m)9(u)-4(n)8(i)3(cat)-9(ion)8( )-12(g)8(a)-12(m)9(e)-12(s)]TJ 0 -1.1566 TD 0.004 Tc 0.035 Tw [(of)12( F)6(o)-2(rg)10(es)7( [1986] an)10(d My)22(ers)7(o)-2(n)10( [1986]. S)6(ee Kan)10(dori)5( [)12(200)10(2] f)12(o)-2(r )-12(a )-12(s)7(u)10(rv)10(e)-10(y)22( )-12(of)12( )-24(s)7(t)5(u)10(d)-2(i)5(e)-10(s)7( )-12(of)12( )-12(repeat)5(ed )-12(g)10(a)-10(m)23(e)-10(s)7( )-24(w)15(i)5(th)]TJ T* 0.005 Tc -0.002 Tw [(pri)6(v)11(at)6(e )-12(m)24(oni)6(t)6(o)-1(ri)6(ng)11(, bot)6(h)11( )-12(w)16(i)6(t)6(h)11( a)-9(n)11(d )-12(w)16(i)6(th)11(ou)11(t)6( co)-13(m)12(m)12(uni)6(cat)6(i)6(o)-1(n)11(.)]TJ ET endstream endobj 29 0 obj << /ProcSet [/PDF /Text ] /Font << /F1 24 0 R /F2 25 0 R /F3 30 0 R /F4 31 0 R >> /ExtGState << /GS1 26 0 R >> >> endobj 32 0 obj << /Length 10490 >> stream BT /F2 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g /GS1 gs 0 Tc 0 Tw (2)Tj -17.75 -3 TD 0.12 Tw [(implies that the strateg)10(i)-2(es h)-10(a)4(ve a )-10(finite-automaton )-10(des)-11(c)4(ription. )-10(Consequentl)-12(y)20(, )-20(when )-10(the)]TJ 0 -1.66 TD 0.21 Tw [(information structure is close )-10(enou)-10(g)10(h)0( to public information, the cur)-7(r)3(ent states )-10(of )-10(th)-10(e)]TJ 0 -1.67 TD -0.001 Tc 0.011 Tw [(automata ar)-8(e almost common knowled)-11(g)9(e. Since )-10(repe)-7(ated )-10(g)9(a)3(mes )-10(with )-10(perf)-8(ect )-10(information)]TJ T* 0.001 Tc 0.239 Tw [(ha)5(ve)5( e)5(f)-6(fic)5(i)-1(e)5(n)1(t e)5(quilibria)5( with finite)5( me)5(mor)-16(y)21(, the)5( Maila)5(th-Morris )-10(re)5(sult )-20(y)21(i)-1(e)5(l)-1(ds )-20(a)5( )-10(folk)]TJ 0 -1.66 TD 0 Tc 0.16 Tw [(theorem )10(for games )10(of almost-pe)-6(rfe)-6(ct, almost-public information, but the h)-20(y)20(pothesis of)]TJ 0 -1.67 TD 0.001 Tc -0.001 Tw [(this the)5(o)1(re)5(m ne)5(e)5(d)1( not be)5( sa)5(tisfie)5(d)1( )-10(for )-10(g)11(e)5(n)-9(e)5(ra)5(l ga)5(me)5(s of a)5(lmost-public)5( informa)5(tion.)]TJ 3 -1.67 TD -0.001 Tc 0.181 Tw [(Our startin)-11(g)9( point is a game of publicl)-23(y)19( observ)-11(e)3(d si)-13(g)9(n)-1(als, and )-10(the )-20(F)5(udenb)-11(er)-8(g)9(,)]TJ /F3 1 Tf -3 -1.66 TD 0 Tc 0.05 Tw [(L)11(e)4(vin)-10(e)4( and Maskin [)-7(1994])-7( \(FL)11(M)-1(\) r)-7(e)4(sult that a folk theorem holds )-10(if )-10(the)-6(r)3(e )-10(is )-10(\223suffi)-12(cient\224)]TJ 0 -1.67 TD 0.71 Tw [(public information. W)-6(h)0(en pla)-6(y)20(e)-6(r)3(s observ)-10(e)4( private si)-12(g)10(n)0(als but mak)-10(e)4( )-10(public)]TJ T* 0.14 Tw [(announcements, there is the possibilit)-12(y)20( of )-10(constru)-10(c)4(ting)10( )-20("FL)11(M)-1(-like")8( )-10(equilibria )-10(in )-10(which)]TJ 0 -1.66 TD -0.001 Tc 0.101 Tw [(the pla)-7(y)19(e)-7(r)2(s\222 )-10(actions depend onl)-23(y)19( on the )-20(announc)-7(ements. )-10(Howev)-11(e)3(r, )-10(the )-20(FL)10(M )-10(techniqu)-11(es)]TJ 0 -1.67 TD 0.171 Tw [(cannot be immediatel)-23(y)19( applied, b)-11(ecaus)-12(e)3( it is necessa)-7(r)-18(y)19( for the )-10(equilibrium to provide)]TJ T* 0.001 Tw [(incentives for the pla)-17(y)19(e)-7(r)2(s to \223r)-8(eport truthfull)-23(y)19(.\224)]TJ 3 -1.66 TD 0.011 Tw [(The basic contribution of this pape)-7(r is to show how )-10(this )-10(can )-10(be )-10(don)-11(e )-10(when )-10(pla)-17(y)19(e)-7(r)2(s)]TJ -3 -1.67 TD -0.002 Tc 0.402 Tw [(recei)-4(v)-12(e)2( )10(si)-4(g)8(n)-12(al)-4(s )10(t)-4(h)-2(at)-4( )10(are)-8( )10(hi)-4(g)8(h)-2(l)-24(y)18( )10(but)-4( not)-4( per)-9(f)1(ect)-4(l)-24(y)18( co)-12(rrel)-14(a)2(t)-4(e)2(d. Al)-4(t)-4(hou)-12(g)8(h)-2( t)-4(h)-2(e resul)-4(t)-4(s)]TJ T* 0.001 Tc 0.119 Tw [(g)11(e)5(n)-9(e)5(ra)5(lize)5( )10(from )10(the)5( )10(two)-9(-)4(pe)5(rson c)5(a)5(s)0(e)5(,)1( )10(in )10(ma)5(n)-19(y)21( re)5(spec)5(ts )10(it is a)5(n)1( a)5(dva)5(ntage)5( to ha)5(ve)5( more)]TJ 0 -1.66 TD [(tha)5(n)1( two play)21(ers, bec)5(a)5(u)1(se)5( it is possible)5( to build e)5(quilibria)5( b)-9(y)21( )-10(c)5(o)1(mpa)5(r)4(in)-9(g)11( )-10(the)5( )-10(re)5(ports )-10(of)]TJ 0 -1.67 TD -0.001 Tc 0.001 Tw [(different pla)-17(y)19(e)-7(r)2(s, and usin)-11(g)9( )-10(\223third parties\224 to )-10(eff)-8(ectivel)-23(y)19( enfo)-11(rc)-7(e contra)-7(cts. F)5(o)-1(r )-10(this )-10(r)-8(eason)]TJ T* 0.011 Tw [(we )10(focus )10(h)-11(e)3(re )10(on th)-11(e two-pla)-17(y)19(e)-7(r)2( cas)-12(e, and show that )-10(even without third parties, w)-9(e)3( hav)-11(e)3( a)]TJ 0 -1.66 TD -0.002 Tc 0.002 Tw [(fol)-4(k)-2( t)-4(h)-2(eorem)-4( when t)-4(h)-12(e pl)-4(a)-18(y)18(ers)-13(\222)1( si)-4(g)8(n)-12(al)-4(s ar)-9(e hi)-4(g)8(h)-2(l)-24(y)18( c)-8(o)-2(rr)-9(el)-4(at)-4(ed.)]TJ /F1 1 Tf 14.04 0 0 14.04 90.09 292.05 Tm -0.002 Tw [(2.)-6( )-8(The M)-7(odel)]TJ /F3 1 Tf 12 0 0 12 126.09 269.01 Tm -0.013 Tc 0.033 Tw [(In)-13( t)-15(h)-13(e)-9( )]TJ /F4 1 Tf 2.58 0 TD -0.001 Tc 0.021 Tw [(stag)-11(e game)]TJ /F3 1 Tf 4.55 0 TD [(, )-10(each of)-8( t)-3(w)1(o pl)-3(a)-17(y)19(e)-7(r)2(s )]TJ /F5 1 Tf 10.62 0 TD -0.12 Tc [(\021\014)-210(\022)]TJ ET q 1 i 317.85 281.01 24.12 -18 re W* n BT /F6 1 Tf 12 0 0 12 317.85 269.01 Tm 0 Tc 0 Tw (I)Tj ET Q q 1 i 326.37 281.01 24.12 -18 re W* n BT /F7 1 Tf 12 0 0 12 326.37 269.01 Tm 0 Tc 0 Tw (\036)Tj ET Q BT /F3 1 Tf 12 0 0 12 356.85 269.01 Tm 0 Tc 0.03 Tw [( simultaneousl)-12(y)30( choos)-11(es an )]TJ /F4 1 Tf 11.27 0 TD 0.001 Tc [(ac)5(tion)]TJ /T1 1 Tf 8.355 0 0 8.355 98.01 245.25 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.97 0 0 11.97 91.77 249.09 Tm (A)Tj /F3 1 Tf 12 0 0 12 104.01 249.09 Tm 0.001 Tc 0.069 Tw [( from a)5( finite)5( se)5(t )]TJ /T2 1 Tf 8.355 0 0 8.355 200.13 245.25 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.975 0 0 11.975 192.81 249.09 Tm (!)Tj /F3 1 Tf 12 0 0 12 206.49 249.09 Tm -0.001 Tc 0.071 Tw [(. W)-7(e)3( refe)-7(r to v)-11(ectors of )-10(actions, one for ea)-7(ch )-10(pla)-17(y)19(e)-7(r)2(, )-10(as )]TJ /F4 1 Tf 22.99 0 TD 0.001 Tc [(profile)5(s)]TJ /F3 1 Tf 3.06 0 TD 0 Tc 0 Tw (.)Tj -35.75 -1.67 TD 0.005 Tc [(Play)25(e)9(r)8( )]TJ /F6 1 Tf 11.931 0 0 11.931 128.25 229.05 Tm 0 Tc (I)Tj /F3 1 Tf 12 0 0 12 135.21 229.05 Tm 0.21 Tw [(\222s pa)-16(y)20(o)0(f)-7(f)3( to an a)-6(c)4(tion profile )]TJ /F6 1 Tf 13.07 0 TD 0 Tw (A)Tj /F3 1 Tf 0.86 0 TD 0.002 Tc 0.208 Tw [( is )]TJ ET q 1 i 332.01 240.09 16.44 -17.04 re W* n BT /F5 1 Tf 12.028 0 0 12.028 332.01 229.05 Tm 0.469 Tc (\010\011)Tj ET Q q 1 i 328.41 234.93 16.8 -11.88 re W* n BT /T3 1 Tf 8.391 0 0 8.391 328.41 225.21 Tm 0 Tc 0 Tw (I)Tj ET Q q 1 i 322.65 240.09 25.8 -17.04 re W* n BT /F6 1 Tf 12.028 0 0 12.028 322.65 229.05 Tm 0.618 Tc (GA)Tj ET Q BT 12 0 0 12 348.45 229.05 Tm -0.001 Tc 0.211 Tw [(. W)-7(e)3( define )]TJ ET 0 G 2 J 0 j 0.588 w 10 M []0 d 1 i 416.85 236.25 m 422.85 236.25 l 475.17 240.33 m 475.17 223.65 l 500.73 240.33 m 500.73 223.65 l S BT /T4 1 Tf 8.363 0 0 8.363 464.61 224.61 Tm 0 Tc 0 Tw (\014)Tj /F5 1 Tf 11.978 0 0 11.978 439.41 229.05 Tm [(MAX)-1974(\010)-473(\011)]TJ /T5 1 Tf 8.363 0 0 8.363 461.85 224.61 Tm 0.27 Tc [(IA)-1016(I)]TJ ET q 415.77 241.05 87.84 -18.12 re W* n BT /F6 1 Tf 11.978 0 0 11.978 415.77 229.05 Tm 4.58 Tc [(GG)3967(A)]TJ ET Q BT /F7 1 Tf 11.978 0 0 11.978 426.57 229.05 Tm 0 Tc (\036)Tj /F3 1 Tf 12 0 0 12 503.61 229.05 Tm 0.22 Tw [(. I)13(n)]TJ -34.46 -1.67 TD -0.001 Tc 0.071 Tw [(addition, )10(each )10(pla)-17(y)19(e)-7(r)2( observ)-11(e)3(s a priv)-11(ate si)-13(g)9(n)-1(al )]TJ /T6 1 Tf 8.355 0 0 8.355 327.93 205.17 Tm 2.941 Tc (II)Tj /F6 1 Tf 11.975 0 0 11.975 322.65 209.01 Tm 1.653 Tc (Z:)Tj ET q 336.09 221.01 24.12 -18.12 re W* n BT /F7 1 Tf 11.975 0 0 11.975 336.09 209.01 Tm 0 Tc 0 Tw (\211)Tj ET Q BT /F3 1 Tf 12 0 0 12 361.41 209.01 Tm 0.002 Tc 0.068 Tw [( a)6( finite)6( se)6(t. We)6( le)6(t )]TJ /T7 1 Tf 8.391 0 0 8.391 493.41 205.05 Tm 1.166 Tc (\021\022)Tj /F5 1 Tf 12.028 0 0 12.028 484.17 209.01 Tm 0.728 Tc [(\010\014)-239(\011)]TJ /F6 1 Tf -1.9055 0 TD 1.844 Tc [(ZZ)1118(Z)]TJ /F7 1 Tf 0.848 0 TD 0 Tc 0 Tw (\036)Tj /F3 1 Tf 12 0 0 12 519.09 209.01 Tm (,)Tj /T8 1 Tf 8.391 0 0 8.391 124.65 185.13 Tm 2.496 Tc (\021\022)Tj /F6 1 Tf 12.028 0 0 12.028 91.17 189.09 Tm 1.544 Tc [(::)80(:)]TJ /F7 1 Tf 1.0775 0 TD 1.485 Tc (\036q)Tj /F3 1 Tf 12 0 0 12 156.09 189.09 Tm -0.001 Tc 0.211 Tw [(. Each a)-7(c)3(tion profile )]TJ /T9 1 Tf 8.355 0 0 8.355 307.17 185.13 Tm 1.216 Tc [(\021\022)-5127(\021)-1264(\022)]TJ /F5 1 Tf 11.975 0 0 11.975 297.45 189.09 Tm 0.763 Tc [(\010\014)-240(\011)]TJ /F6 1 Tf -1.9842 0 TD 1.774 Tc [(AA)1103(A)-280(!)371(!)452(!)]TJ /F7 1 Tf 0.9219 0 TD 3.379 Tc [(\036\211)2046(\036)1904(q)]TJ /F3 1 Tf 12 0 0 12 410.97 189.09 Tm 0.001 Tc 0.209 Tw [( induc)5(e)5(s)0( a)5( proba)5(bilit)-21(y)]TJ -26.74 -1.67 TD (distribution )Tj /T10 1 Tf 8.348 0 0 8.348 157.29 166.65 Tm 0 Tc 0 Tw (A)Tj /F8 1 Tf 11.963 0 0 11.963 151.17 169.05 Tm (Q)Tj /F3 1 Tf 12 0 0 12 164.49 169.05 Tm -0.002 Tc 0.092 Tw [( over )]TJ /F4 1 Tf 2.45 0 TD -0.001 Tc [(outcome)-7(s)]TJ /F3 1 Tf 3.78 0 TD 0 Tc 0 Tw ( )Tj /F6 1 Tf 0.54 0 TD (Z)Tj /F3 1 Tf 0.73 0 TD -0.001 Tc 0.101 Tw [(. )10( )10(At )10(the )10(end of ea)-7(ch sta)-7(g)9(e of th)-11(e )-10(g)9(a)3(me, pla)-17(y)19(e)-7(r)2(s make)]TJ /F4 1 Tf -13.7 -1.67 TD (announcements)Tj /F3 1 Tf 6.21 0 TD 0 Tc 0 Tw ( )Tj /F5 1 Tf 12.028 0 0 12.028 206.97 149.01 Tm (\012)Tj /T11 1 Tf 8.391 0 0 8.391 175.29 145.17 Tm (I)Tj /F6 1 Tf 12.028 0 0 12.028 169.41 149.01 Tm 1.486 Tc (Y9)Tj /F7 1 Tf 1.1573 0 TD 0 Tc (\211)Tj /F3 1 Tf 12 0 0 12 214.29 149.01 Tm -0.002 Tc 0.052 Tw (, where )Tj /F5 1 Tf 11.963 0 0 11.963 266.85 149.01 Tm 0 Tc 0 Tw (\012)Tj /F6 1 Tf -1.1335 0 TD (9)Tj /F3 1 Tf 12 0 0 12 274.77 149.01 Tm 0.001 Tc 0.059 Tw [( )10(is a)5( finite)5( se)5(t tha)5(t)-1( is the)5( sa)5(me)5( fo)-9(r e)5(a)-5(c)5(h)1( pla)-15(y)21(er.)]TJ /F2 1 Tf 8.04 0 0 8.04 501.93 154.53 Tm 0 Tc 0 Tw (5)Tj /F3 1 Tf 12 0 0 12 506.01 149.01 Tm 0.06 Tc ( A)Tj -34.66 -2.25 TD 0 Tc ( )Tj ET 90.09 125.13 143.88 -0.48 re f BT /F2 1 Tf 6.48 0 0 6.48 90.09 113.49 Tm (5)Tj 9.96 0 0 9.96 93.33 108.93 Tm 0.002 Tc 0.085 Tw [( )12(T)-14(h)8(e assum)21(p)-4(t)-9(i)3(on)8( t)-9(h)8(at th)8(e t)-21(w)25(o pla)-12(y)8(ers h)8(a)-12(v)8(e)0( t)-9(h)8(e sa)-12(m)9(e)0( sets o)-16(f)10( possible ann)8(oun)8(ce)-12(m)9(e)0(n)8(t)-9(s is )-12(m)9(o)-4(tivated b)-16(y)20( ou)8(r)]TJ -0.3253 -1.1446 TD 0.005 Tc 0.179 Tw [(f)13(o)-1(cus)8( on)11( alm)24(o)-13(s)8(t)-6(-)13(p)-1(u)11(b)-1(l)6(i)6(c)3( i)6(n)-1(f)13(o)-1(r)-11(m)24(a)-9(t)6(i)6(o)-1(n)11(.)2( )-12(A)16(l)6(th)11(ough)11( )-12(w)16(e)3( can)11( alw)16(a)-9(y)11(s)8( in)11(creas)8(e th)11(e s)8(i)6(ze of)13( th)11(e sm)12(all)6(e)3(r )-24(m)24(e)3(ss)8(ag)11(e)]TJ 0 -1.1566 TD 0.001 Tc 0.05 Tw [(space, doin)7(g)7( so inv)7(o)-5(lv)7(e)-13(s)4( a loss of)9( )-12(g)7(e)-13(n)7(e)-1(ralit)-10(y)19( beca)-13(u)7(s)4(e i)-10(n)7(creasing)7( t)-10(h)7(e possible )-12(m)8(e)-1(ssa)-13(g)7(e)-1(s ca)-13(n)7( )-12(increase )-12(th)7(e )-24(set)]TJ T* 0 Tc 0.003 Tw [(o)-6(f)8( p)-6(o)-6(t)1(ential eq)-6(uilib)-6(ria.)]TJ ET endstream endobj 33 0 obj << /ProcSet [/PDF /Text ] /Font << /F1 24 0 R /F2 25 0 R /F3 30 0 R /F4 31 0 R /F5 34 0 R /F6 35 0 R /F7 36 0 R /F8 37 0 R /T1 38 0 R /T2 39 0 R /T3 40 0 R /T4 41 0 R /T5 42 0 R /T6 43 0 R /T7 44 0 R /T8 45 0 R /T9 46 0 R /T10 47 0 R /T11 48 0 R >> /ExtGState << /GS1 26 0 R >> >> endobj 49 0 obj << /Length 14538 >> stream BT /F2 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g /GS1 gs 0 Tc 0 Tw (3)Tj /F4 1 Tf -17.75 -3 TD 0.1 Tw [(profile of announcements)]TJ /F2 1 Tf 10.36 0 TD 0.002 Tc 0.098 Tw [( is )-10(a)6( )]TJ /F5 1 Tf 11.97 0 0 11.97 302.25 704.01 Tm 1.787 Tc (\012\012)Tj /F6 1 Tf -5.0528 0 TD 1.205 Tc [(Y9)-263(9)-343(9)]TJ /F7 1 Tf 0.8722 0 TD 1.404 Tc [(\211\036)-553(q)]TJ /F2 1 Tf 12 0 0 12 337.65 704.01 Tm -0.001 Tc 0.111 Tw [(. A stag)9(e )-10(game strat)-13(e)3(g)-11(y)19( )-10(for pla)-17(y)19(e)-7(r)2( )]TJ /F6 1 Tf 14.63 0 TD 0 Tc 0 Tw (I)Tj /F2 1 Tf 0.49 0 TD (,)Tj /F5 1 Tf 11.975 0 0 11.975 117.93 684.09 Tm 0.723 Tc [(\010\014)-510(\011)]TJ /T12 1 Tf 8.355 0 0 8.355 96.93 680.25 Tm 3.387 Tc [(II)1595(I)]TJ /F6 1 Tf 11.975 0 0 11.975 92.01 684.09 Tm 2.054 Tc [(SA)1393(M)]TJ /F7 1 Tf 1.1023 0 TD 0 Tc (\036)Tj /F2 1 Tf 12 0 0 12 156.09 684.09 Tm -0.002 Tc 0.202 Tw [(, i)-4(s)-3( a choi)-4(ce of st)-4(a)-8(g)-2(e )-10(g)8(a)2(m)-4(e)2( )-10(act)-4(i)-4(on )]TJ /T13 1 Tf 8.355 0 0 8.355 344.85 680.25 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.97 0 0 11.97 338.61 684.09 Tm (A)Tj /F2 1 Tf 12 0 0 12 350.85 684.09 Tm -0.001 Tc 0.211 Tw [( and a map )]TJ /F5 1 Tf 12.028 0 0 12.028 435.09 684.09 Tm 3.941 Tc (\032\012)Tj /T14 1 Tf 8.391 0 0 8.391 427.05 680.25 Tm 2.356 Tc (II)Tj ET q 1 i 417.33 695.13 75.96 -17.04 re W* n BT /F6 1 Tf 12.028 0 0 12.028 417.33 684.09 Tm 1.203 Tc [(M:)-700(9)]TJ ET Q BT /F7 1 Tf 12.028 0 0 12.028 457.77 684.09 Tm 0 Tc 0 Tw (l)Tj /F2 1 Tf 12 0 0 12 493.29 684.09 Tm -0.002 Tc 0.212 Tw [( from)]TJ -33.6 -1.67 TD -0.001 Tc 0.031 Tw [(private sig)9(n)-11(al to announcem)-13(ents. W)-7(e)3( ref)-8(e)3(r to )]TJ /T15 1 Tf 8.391 0 0 8.391 353.25 660.09 Tm 1.681 Tc (\021\022)Tj ET q 1 i 339.69 675.09 42.6 -17.04 re W* n BT /F5 1 Tf 12.028 0 0 12.028 339.69 664.05 Tm 1.088 Tc [(\010\014)-238(\011)]TJ ET Q BT /F6 1 Tf 12.028 0 0 12.028 312.33 664.05 Tm 1.782 Tc [(MM)1098(M)]TJ ET q 1 i 326.97 675.09 24.12 -17.04 re W* n BT /F7 1 Tf 12.028 0 0 12.028 326.97 664.05 Tm 0 Tc 0 Tw (\036)Tj ET Q BT /F2 1 Tf 12 0 0 12 382.29 664.05 Tm 0.002 Tc 0.028 Tw [( a)6(s)1( a)6( me)6(ssag)12(e)6( pro)-8(f)5(ile)6(. We)6( )-10(le)6(t)]TJ /T13 1 Tf 8.355 0 0 8.355 99.09 640.17 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.975 0 0 11.975 92.13 644.01 Tm (3)Tj /F2 1 Tf 12 0 0 12 105.09 644.01 Tm -0.002 Tc 0.002 Tw [( denote the spac)-8(e of pla)-18(y)18(er)-9( )]TJ /F6 1 Tf 11.03 0 TD 0 Tc 0 Tw (I)Tj /F3 1 Tf 0.49 0 TD -0.001 Tc 0.001 Tw [(\222s st)-3(age )-10(g)9(a)3(m)-3(e)3( st)-3(r)-8(a)3(t)-3(e)-7(g)9(i)-3(es.)]TJ -9.77 -1.66 TD -0.002 Tc 0.022 Tw [(I)11(n)-2( t)-4(h)-2(e )-10(rep)-12(eat)-4(ed )-10(gam)-4(e)2(, i)-4(n)-2( ea)-8(ch peri)-4(od )]TJ /F5 1 Tf 16.88 0 TD -0.12 Tc [(\021\014)-210(\022)-40(\014)]TJ /F6 1 Tf -1.81 0 TD 0 Tc 0 Tw (T)Tj ET q 1 i 315.93 636.09 24.12 -18 re W* n BT /F7 1 Tf 12 0 0 12 315.93 624.09 Tm (\036)Tj ET Q BT /F9 1 Tf 12 0 0 12 346.65 624.09 Tm (!)Tj /F3 1 Tf 1.2 0 TD 0.001 Tc 0.029 Tw [(, )10(the)5( )10(sta)5(g)1(e)5( g)11(a)5(me)5( is pla)-15(y)21(ed. At the)]TJ -22.58 -1.67 TD -0.001 Tc 0.351 Tw [(start of ea)-7(ch period, )-10(a public randomiz)-7(ation )]TJ /F5 1 Tf 22.25 0 TD 0.02 Tc [(;\020)100(\014)-40(\021)50(=)]TJ ET q 1 i 333.45 616.05 24 -18 re W* n BT /F6 1 Tf 12 0 0 12 333.45 604.05 Tm 0 Tc 0 Tw (W)Tj ET Q BT /F7 1 Tf 12 0 0 12 346.17 604.05 Tm 0 Tc 0 Tw (\211)Tj /F3 1 Tf 2.85 0 TD -0.001 Tc 0.361 Tw [( )10(is drawn from )-10(a uniform)]TJ -24.19 -1.67 TD 0 Tc 0.23 Tw (distribution. The )Tj /F4 1 Tf 7.38 0 TD 0.001 Tc [(public history)]TJ /F3 1 Tf 5.76 0 TD 0.002 Tc 0.238 Tw [( a)6(t)0( time)6( )]TJ /F6 1 Tf 4.03 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 0.6 0 TD (, )Tj ET q 1 i 320.13 594.81 15.12 -13.68 re W* n BT /F2 1 Tf 11.97 0 0 11.97 320.13 584.01 Tm 0.389 Tc (\(\))Tj ET Q BT /F4 1 Tf 11.97 0 0 11.97 314.01 584.01 Tm 0.372 Tc (ht)Tj /F3 1 Tf 12 0 0 12 335.25 584.01 Tm -0.001 Tc 0.241 Tw [(, consists of the announcements and)]TJ -20.43 -1.66 TD 0.001 Tw [(realiz)-7(ation of )]TJ /F4 1 Tf 5.55 0 TD 0.003 Tc (w )Tj /F3 1 Tf 0.92 0 TD 0 Tc 0 Tw [(sig)10(n)0(als in all previous pe)-6(riods, and also the r)-7(ealiz)-6(ation of )]TJ /F4 1 Tf 23.02 0 TD 0.003 Tc (w )Tj /F3 1 Tf 0.92 0 TD 0 Tc (in period )Tj /F4 1 Tf 3.83 0 TD 0.001 Tc (t, )Tj /F3 1 Tf 0.78 0 TD (so)Tj /F5 1 Tf 11.97 0 0 11.97 174.33 542.85 Tm -0.008 Tc [(\010)-341(\011)-1363(\010)-632(\010)50(\021)51(\011)-10(\014)-570(\010)50(\021)41(\011)0(\014)-771(\010)30(\022)21(\011)-10(\014)-580(\010)40(\022)11(\011)0(\014)-1051(\014)-761(\010)-1554(\021)51(\011\014)-580(\010)-1544(\021)41(\011\014)-771(\010)-341(\011)0(\011)]TJ /F6 1 Tf -0.5314 0 TD 0.342 Tc [(HT)-1804(W)-1194(Y)-1174(W)-1254(Y)-2548(WT)-2125(Y)19(T)-2125(WT)]TJ /F7 1 Tf 1.9349 0 TD 12.103 Tc [(\036\016)9276(\016)]TJ /F9 1 Tf 9.8851 0 TD 0 Tc (!)Tj /F3 1 Tf 12 0 0 12 442.05 542.85 Tm (.)Tj -29.33 -2.25 TD -0.002 Tc (The )Tj /F4 1 Tf 1.8 0 TD 0 Tc (private history)Tj /F3 1 Tf 5.86 0 TD -0.001 Tc 0.001 Tw [( for pla)-17(y)19(e)-7(r)2( )]TJ /F6 1 Tf 11.931 0 0 11.931 237.09 515.85 Tm 0 Tc 0 Tw (I)Tj /F3 1 Tf 12 0 0 12 244.05 515.85 Tm 0.001 Tc -0.001 Tw [( a)5(t)-1( time)5( )]TJ /F6 1 Tf 11.931 0 0 11.931 284.97 515.85 Tm 0 Tc 0 Tw (T)Tj /F3 1 Tf 12 0 0 12 293.01 515.85 Tm 0.001 Tc -0.001 Tw ( is)Tj /F5 1 Tf 11.97 0 0 11.97 182.37 494.61 Tm -0.049 Tc [(\010)-382(\011)-1404(\010)-773(\010)19(\021\011)-41(\014)-882(\010)9(\021\011)-41(\014)-902(\010)-11(\022)-30(\011)-41(\014)-882(\010)-11(\022)-30(\011)-41(\014)-1082(\014)-912(\010)-1585(\021)10(\011)-51(\014)-882(\010)-1585(\021)10(\011)-51(\011)]TJ /T16 1 Tf 8.355 0 0 8.355 178.77 492.21 Tm 4.823 Tc [(II)1867(I)1853(I)1795(I)-129(I)-416(I)]TJ /F6 1 Tf 11.97 0 0 11.97 173.01 494.61 Tm 0.592 Tc [(HT)-1524(A)-1243(Z)-1213(A)-1303(Z)-2586(A)-20(T)-1895(Z)-60(T)]TJ /F7 1 Tf 2.1855 0 TD 12.915 Tc [(\036\016)9827(\016)]TJ ET q 1 i 326.01 505.53 24 -15.96 re W* n BT /F9 1 Tf 11.97 0 0 11.97 326.01 494.61 Tm 0 Tc 0 Tw (!)Tj ET Q BT /F3 1 Tf 12 0 0 12 437.01 494.61 Tm 0 Tc 0 Tw (.)Tj -28.91 -2.25 TD -0.002 Tc (A )Tj /F4 1 Tf 1.13 0 TD 0 Tc (strategy )Tj /F3 1 Tf 3.63 0 TD -0.001 Tc 0.161 Tw [(for pla)-17(y)19(e)-7(r)2( )]TJ /F6 1 Tf 11.931 0 0 11.931 203.13 467.61 Tm 0 Tc 0 Tw (I)Tj /F3 1 Tf 12 0 0 12 210.09 467.61 Tm -0.001 Tc 0.161 Tw [( is a sequence o)-11(f)2( maps )]TJ /F5 1 Tf 11.975 0 0 11.975 344.97 467.61 Tm 0.312 Tc (\010\011)Tj /T17 1 Tf 8.355 0 0 8.355 341.25 463.77 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.975 0 0 11.975 348.69 467.61 Tm (T)Tj ET q 1 i 334.65 479.61 24 -18.36 re W* n BT /F8 1 Tf 11.975 0 0 11.975 334.65 467.61 Tm (T)Tj ET Q BT /F3 1 Tf 12 0 0 12 360.21 467.61 Tm 0.16 Tw [( mapping)10( the public and )-10(p)-10(r)3(ivate)]TJ -22.51 -1.66 TD (histories )Tj /F5 1 Tf 11.97 0 0 11.97 141.45 447.69 Tm 0.333 Tc [(\010\011)341(\014)-520(\010)0(\011)]TJ /T18 1 Tf 8.355 0 0 8.355 164.73 445.29 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.97 0 0 11.97 135.09 447.69 Tm 0.341 Tc [(HT)-472(H)-241(T)]TJ /F3 1 Tf 12 0 0 12 183.09 447.69 Tm 0 Tc 0.03 Tw [( to proba)4(bilit)-12(y)20( distributions ove)4(r )]TJ /T19 1 Tf 8.355 0 0 8.355 352.17 443.85 Tm 0 Tw (I)Tj /F6 1 Tf 11.975 0 0 11.975 345.21 447.69 Tm (3)Tj /F3 1 Tf 12 0 0 12 358.17 447.69 Tm -0.001 Tc 0.031 Tw (. A )Tj /F4 1 Tf 1.53 0 TD 0.001 Tc 0.029 Tw [(partial strate)5(gy)]TJ /F3 1 Tf 6.23 0 TD [( is the)5( )-10(stra)5(teg)-9(y)]TJ -30.1 -1.67 TD 0 Tc 0.28 Tw [(conditional )10(on )10(the )10(initial )10(realization of the public randomization device. A )]TJ /F4 1 Tf 33.5 0 TD 0.001 Tc (public)Tj -33.5 -1.67 TD 0 Tc (strategy )Tj /F3 1 Tf 3.56 0 TD 0.09 Tw [(is a strate)-6(g)-10(y)20( that depe)-6(nds onl)-12(y)20( on )]TJ /F5 1 Tf 14.91 0 TD 0.321 Tc (\010\011)Tj /F6 1 Tf -0.53 0 TD 0.339 Tc (HT)Tj /F3 1 Tf 1.83 0 TD -0.001 Tc 0.101 Tw [(. )10(W)-7(e)3( )10(denote the null private history)9( )-10(fo)-11(r)]TJ -19.77 -1.66 TD 0.006 Tc [(p)6(l)4(ay)26(er)9( )]TJ /F4 1 Tf 2.81 0 TD 0.002 Tc (i )Tj /F3 1 Tf 0.6 0 TD 0.02 Tc [(by)40( )]TJ /F2 1 Tf 2.2 0 TD -0.053 Tc [(\(1)17(\))]TJ /F4 1 Tf 6.938 0 0 6.938 154.05 384.57 Tm 0 Tc 0 Tw (i)Tj 12 0 0 12 148.77 387.69 Tm (h)Tj /F3 1 Tf 1.93 0 TD 0.07 Tw [(; the initial public his)9(t)-2(or)-7(y)20( is )]TJ ET q 1 i 320.25 398.49 14.04 -13.68 re W* n BT /F2 1 Tf 11.97 0 0 11.97 320.25 387.69 Tm -0.052 Tc [(\(1)17(\))]TJ ET Q BT /F4 1 Tf 11.97 0 0 11.97 314.13 387.69 Tm 0 Tw (h)Tj /F3 1 Tf 12 0 0 12 334.29 387.69 Tm -0.001 Tc 0.081 Tw [(. Observ)-11(e that for )-10(each public history)]TJ /F5 1 Tf 11.97 0 0 11.97 97.41 367.65 Tm 0.333 Tc (\010\011)Tj /F6 1 Tf -0.5313 0 TD 0.341 Tc (HT)Tj /F3 1 Tf 12 0 0 12 112.05 367.65 Tm 0.001 Tc 0.079 Tw [( the)5( public)5( profile)5( )]TJ /F8 1 Tf 7.91 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 0.88 0 TD -0.001 Tc 0.091 Tw [( induces )-10(a partial pro)-11(f)2(ile over the)-7( rep)-11(eated )-10(game be)-7(g)9(i)-3(nning)9( at)]TJ /F6 1 Tf 11.931 0 0 11.931 92.01 347.61 Tm 0 Tc 0 Tw (T)Tj /F3 1 Tf 12 0 0 12 100.05 347.61 Tm 0.21 Tw [(. W)-6(e)4( denote this b)-10(y)20( )]TJ /F7 1 Tf 12.081 0 0 11.97 209.25 347.61 Tm 3.228 Tc (<>)Tj /F5 1 Tf 11.97 0 0 11.97 224.97 347.61 Tm 0.752 Tc [(\\\010)419(\011)]TJ /F6 1 Tf 0.5113 0 TD 0.331 Tc (HT)Tj /F8 1 Tf -1.4136 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 12 0 0 12 255.69 347.61 Tm (.)Tj /F10 1 Tf 0.25 0 TD ( )Tj /F3 1 Tf 0.46 0 TD -0.001 Tc 0.211 Tw [(Given a private p)-11(a)3(rtial profile )]TJ /F8 1 Tf 13.38 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 0.88 0 TD -0.001 Tc 0.221 Tw [(, we c)-7(a)3(n use the)]TJ -28.77 -1.66 TD 0.001 Tc 0.209 Tw [(proba)5(bilit)-11(y)21( distribution g)11(e)5(n)-9(e)5(ra)5(te)5(d b)-19(y)21( the)5( partia)5(l profile)5( a)5(nd )-10(the)5( )-10(null )-10(initia)5(l )-10(history)21( )-10(to)]TJ 0 -1.67 TD -0.002 Tc 0.262 Tw [(com)-4(put)-4(e for e)-8(ach pl)-4(a)-18(y)18(e)-8(r)1( )]TJ /F6 1 Tf 11.931 0 0 11.931 223.89 307.65 Tm 0 Tc 0 Tw (I)Tj /F3 1 Tf 12 0 0 12 230.85 307.65 Tm -0.001 Tc 0.261 Tw [( an ex)-11(pected av)-11(era)-7(g)-1(e prese)-7(n)-1(t )-10(value )-10(with )-10(discount )-10(fac)-7(t)-3(or)]TJ /F5 1 Tf 12.028 0 0 12.028 92.73 287.61 Tm 3.231 Tc (\020\021)Tj /F8 1 Tf 1.8856 0 TD 0 Tc 0 Tw (E)Tj /F7 1 Tf -1.0775 0 TD 1.108 Tc (b\035)Tj /F3 1 Tf 12 0 0 12 146.13 287.61 Tm 0 Tc 0.01 Tw [(. W)-6(e)4( denote this b)-10(y)20( )]TJ /F5 1 Tf 11.975 0 0 11.975 256.77 287.61 Tm 0.513 Tc [(\010\014)-69(\011)]TJ /T20 1 Tf 8.355 0 0 8.355 253.05 283.77 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.975 0 0 11.975 243.81 287.61 Tm (')Tj /F8 1 Tf 1.443 0 TD 0.361 Tc (TE)Tj /F3 1 Tf 12 0 0 12 284.73 287.61 Tm -0.001 Tc 0.011 Tw (. A )Tj /F4 1 Tf 1.49 0 TD 0.001 Tc 0.009 Tw [(pe)5(rfe)5(c)5(t)-1( public)5( e)5(quilibrium)]TJ /F3 1 Tf 10.46 0 TD [( is a)5( )-10(public)5( )-10(stra)5(teg)-9(y)]TJ -28.17 -1.66 TD -0.001 Tc (profile )Tj /F8 1 Tf 3.12 0 TD 0 Tc 0 Tw (T)Tj /F3 1 Tf 0.88 0 TD -0.001 Tc 0.001 Tw [( such that )-10(for )-10(an)-21(y)19( )-10(public )-10(histor)-18(y)19( )]TJ /F5 1 Tf 11.97 0 0 11.97 301.65 267.69 Tm 0.333 Tc (\010\011)Tj /F6 1 Tf -0.5313 0 TD 0.341 Tc (HT)Tj /F3 1 Tf 12 0 0 12 316.29 267.69 Tm 0.001 Tc 0.009 Tw [( a)5(nd a)5(n)-19(y)21( p)-9(r)4(iva)5(t)-1(e)5( p)-9(a)5(rtia)5(l stra)5(teg)-9(y)21( )]TJ /T21 1 Tf 8.379 0 0 8.379 480.69 263.97 Tm 0 Tc 0 Tw (I)Tj /F8 1 Tf 12 0 0 12 474.09 267.69 Tm (T)Tj /F9 1 Tf 0.12 0.03 TD (\004)Tj /F3 1 Tf 0.93 -0.03 TD 0.01 Tc [( by)30( )-10(a)14(n)0(y)]TJ -33.05 -1.67 TD 0.006 Tc [(p)6(l)4(ay)26(er)9( )]TJ /F6 1 Tf 11.931 0 0 11.931 125.13 247.65 Tm 0 Tc (I)Tj /F3 1 Tf 12 0 0 12 132.09 247.65 Tm -0.001 Tc 0.001 Tw ( we have)Tj /F7 1 Tf 12.073 0 0 11.97 218.01 226.41 Tm 3.221 Tc [(<>)-2296(<)-785(>)]TJ 7.6537 0 TD 5.854 Tc (\011\012)Tj /F5 1 Tf 11.97 0 0 11.97 214.41 226.41 Tm 1.215 Tc [(\010\\)453(\010)882(\011)852(\014)613(\011)-1083(\010)-50(\014)-931(\\)453(\010)882(\011)411(\014)613(\011)]TJ /T22 1 Tf 8.355 0 0 8.355 210.81 224.01 Tm 10.711 Tc [(II)8631(I)8042(I)]TJ /F6 1 Tf 11.97 0 0 11.97 201.69 226.41 Tm 2.406 Tc [('H)2075(T)-933(')-2476(H)2075(T)]TJ /F8 1 Tf 1.7645 0 TD 3.239 Tc [(TE)-312(T)2236(T)-1233(E)]TJ /T23 1 Tf 8.355 0 0 8.355 341.61 224.01 Tm 0 Tc 0 Tw (\016)Tj /F7 1 Tf 11.97 0 0 11.97 281.97 226.41 Tm (p)Tj ET q 1 i 317.61 237.33 24.12 -15.96 re W* n BT /F9 1 Tf 11.97 0 0 11.97 317.61 226.65 Tm (\004)Tj ET Q BT /F3 1 Tf 12 0 0 12 407.61 226.41 Tm (.)Tj -26.46 -2.25 TD 0.001 Tc 0.289 Tw [(Note)5( tha)5(t)-1( b)-9(y)21( sta)5(n)1(d)-9(a)5(rd d)-19(y)21(n)-9(a)5(mic)5( pro)-9(g)11(ra)5(mming)11( arg)11(u)1(me)5(nts it is suffic)5(i)-1(e)5(n)1(t )-10(to )-10(c)5(onside)5(r)]TJ 0 -1.66 TD 0 Tc 0 Tw [(deviations to public strateg)10(i)-12(es.)]TJ /F1 1 Tf 0 -2.67 TD 0.001 Tc 0.001 Tw [(3. The )10(Structure of Information)]TJ /F3 1 Tf 3 -1.92 TD 0 Tc 0.01 Tw [(Given our assumption of a common announ)-10(cement spa)-6(ce, it is )-10(convenient )-10(to )-10(think)]TJ -3 -1.66 TD -0.001 Tc 0.061 Tw [(of )10(pla)-7(y)19(e)-7(r)2(s )10(a)-7(g)-1(re)-7(eing)9( )10(if )10(th)-11(ey)9( )10(m)-13(a)3(ke the s)-12(a)3(me announ)-11(cement as )-10(ea)-7(ch other. W)-7(e)3( c)-7(a)3(n think of)]TJ /F5 1 Tf 11.963 0 0 11.963 103.53 84.45 Tm 0 Tc 0 Tw (\012)Tj /F6 1 Tf -1.1636 0 TD (9)Tj /F3 1 Tf 12 0 0 12 111.09 84.45 Tm -0.001 Tc 0.041 Tw [( as being)9( th)-11(e subset of )]TJ /F6 1 Tf 11.963 0 0 11.963 222.81 84.45 Tm 0 Tc 0 Tw (9)Tj /F3 1 Tf 12 0 0 12 236.25 84.45 Tm 0.001 Tc 0.049 Tw [( in whic)5(h )]TJ /T24 1 Tf 8.324 0 0 8.324 292.41 80.49 Tm 2.852 Tc (\021\022)Tj /F6 1 Tf 11.931 0 0 11.931 286.77 84.45 Tm 1.824 Tc (YY)Tj /F7 1 Tf 1.227 0 TD 0 Tc 0 Tw (\036)Tj /F3 1 Tf 12 0 0 12 326.73 84.45 Tm 0.05 Tw [(, a)4(nd refe)4(r to this a)4(s)-1( the)4( )]TJ /F4 1 Tf 9.95 0 TD (diagonal)Tj /F3 1 Tf 3.56 0 TD -0.002 Tc 0.052 Tw [( of )]TJ /F6 1 Tf 11.963 0 0 11.963 505.65 84.45 Tm 0 Tc 0 Tw (9)Tj /F3 1 Tf 12 0 0 12 519.09 84.45 Tm (.)Tj ET endstream endobj 50 0 obj << /ProcSet [/PDF /Text ] /Font << /F1 24 0 R /F2 25 0 R /F3 30 0 R /F4 31 0 R /F5 34 0 R /F6 35 0 R /F7 36 0 R /F8 37 0 R /F9 51 0 R /F10 52 0 R /T12 53 0 R /T13 54 0 R /T14 55 0 R /T15 56 0 R /T16 57 0 R /T17 58 0 R /T18 59 0 R /T19 60 0 R /T20 61 0 R /T21 62 0 R /T22 63 0 R /T23 64 0 R /T24 65 0 R >> /ExtGState << /GS1 26 0 R >> >> endobj 67 0 obj << /Length 12401 >> stream BT /F2 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g /GS1 gs 0 Tc 0 Tw (4)Tj -17.75 -3 TD -0.001 Tc 0.071 Tw [(Given a messa)-7(ge profile )]TJ /F6 1 Tf 11.952 0 0 11.952 213.81 704.01 Tm 0 Tc 0 Tw (M)Tj /F2 1 Tf 12 0 0 12 226.65 704.01 Tm -0.001 Tc 0.071 Tw (, the information structure )Tj /F8 1 Tf 11.952 0 0 11.952 359.97 704.01 Tm 0 Tc 0 Tw (Q)Tj /F2 1 Tf 12 0 0 12 369.33 704.01 Tm 0.07 Tw [( induces a )-10(distribution )-10(over )-10(the)]TJ -23.27 -1.66 TD -0.001 Tc 0.001 Tw [(diag)9(on)-11(al of announc)-7(ement profiles. W)-7(e)3( de)-7(note b)-21(y)]TJ 10.46 -1.92 TD 0 Tc 0 Tw ( )Tj /T25 1 Tf 6 0 0 6 301.41 652.65 Tm 1.18 Tc [(\021\021)-1660(\022)-80(\022)]TJ /T26 1 Tf 8.379 0 0 8.379 293.01 655.41 Tm 1.128 Tc [(\\\010)288(\011)-887(\010)230(\011)-214(\012)]TJ /F5 1 Tf 12 0 0 12 235.29 661.05 Tm 0.471 Tc [(\010\012)470(\011)-9680(\010)40(\011)]TJ /T27 1 Tf 8.379 0 0 8.379 227.25 665.73 Tm 0 Tc (M)Tj -0.1003 -0.845 TD 16.922 Tc (AA)Tj 7.4616 -0.3867 TD 0.281 Tc [(ZM)-468(Z)-1289(M)-526(Z)-1347(Y)]TJ /F6 1 Tf 12 0 0 12 239.25 661.05 Tm 11.421 Tc (YZ)Tj /F8 1 Tf -1.58 0 TD 11.608 Tc (QQ)Tj /T28 1 Tf 8.379 0 0 8.379 318.21 655.41 Tm 2.898 Tc (\036\036)Tj /F7 1 Tf 12 0 0 12 259.65 661.05 Tm 0 Tc (\036)Tj 18 0 0 18 273.21 658.29 Tm (\234)Tj /F2 1 Tf 12 0 0 12 393.57 661.05 Tm (,)Tj -25.29 -2.75 TD [(the probabilit)-12(y)20( of th)-10(e diagonal point )]TJ /F5 1 Tf 11.97 0 0 11.97 266.85 628.05 Tm 0.473 Tc [(\010\012)471(\014)-139(\012)471(\011)]TJ /F6 1 Tf 0.3308 0 TD 0.905 Tc (YY)Tj /F2 1 Tf 12 0 0 12 305.97 628.05 Tm -0.001 Tc 0.001 Tw [(, and b)-21(y)]TJ ET 0 G 2 J 0 j 0.588 w 10 M []0 d 1 i 309.09 602.01 m 380.25 602.01 l S BT /T29 1 Tf 8.386 0 0 8.386 341.85 584.13 Tm 0 Tc 0 Tw (\012)Tj ET q 341.97 618.09 40.32 -17.52 re W* n BT /F5 1 Tf 12.012 0 0 12.012 341.97 606.69 Tm 0.47 Tc [(\010\012)470(\011)]TJ ET Q BT /F5 1 Tf 12.012 0 0 12.012 246.21 599.01 Tm 0.47 Tc [(\010\012)200(\\)-528(\012)470(\011)]TJ 9.9499 -0.7692 TD (\010\011)Tj ET q 334.05 618.09 16.8 -10.92 re W* n BT /T30 1 Tf 8.386 0 0 8.386 334.05 611.37 Tm 0 Tc (M)Tj ET Q BT /T30 1 Tf 8.386 0 0 8.386 333.09 604.29 Tm 0 Tc (A)Tj -11.3183 -0.0572 TD (M)Tj -0.1002 -0.8442 TD (A)Tj 14.3517 -0.2576 TD (M)Tj -0.1145 -0.8585 TD (A)Tj ET q 324.81 593.85 25.92 -13.8 re W* n BT 8.386 0 0 8.386 324.81 584.13 Tm 0.595 Tc (Y9)Tj ET Q BT /F6 1 Tf 12.012 0 0 12.012 345.93 606.69 Tm (Y)Tj -7.9719 -0.6393 TD 1.199 Tc (Y9)Tj 9.9499 -0.7692 TD 0 Tc (Y)Tj ET q 326.97 618.09 24 -17.76 re W* n BT /F8 1 Tf 12.012 0 0 12.012 326.97 606.69 Tm (Q)Tj ET Q BT /F8 1 Tf 12.012 0 0 12.012 231.21 599.01 Tm (Q)Tj 9.9399 -0.7692 TD (Q)Tj ET q 329.61 594.21 16.8 -14.16 re W* n BT /T31 1 Tf 8.386 0 0 8.386 329.61 584.13 Tm (\211)Tj ET Q BT /F7 1 Tf 12.012 0 0 12.012 295.17 599.01 Tm (\036)Tj 18.019 0 0 18.019 309.33 587.01 Tm (\234)Tj /F2 1 Tf 12 0 0 12 90.09 558.09 Tm 0.17 Tw [(the )10(probabilit)-12(y)20( conditional on the diag)10(on)-10(al of the joint announcement )]TJ /F5 1 Tf 11.97 0 0 11.97 457.05 558.09 Tm 0 Tw (\012)Tj /F6 1 Tf -0.802 0 TD (Y)Tj /F2 1 Tf 12 0 0 12 464.37 558.09 Tm 0.17 Tw [(. )-10(I)23(t)-2( is also)]TJ /F3 1 Tf -31.19 -1.67 TD 0 Tw [(convenient to define th)-10(e probabilit)-12(y)20( o)-10(f)3( the opponent\222s m)-12(e)4(ssag)10(e)4( )-10(g)10(i)-2(ven )-10(a pla)-16(y)20(er\222s si)-12(g)10(n)0(al)]TJ /T32 1 Tf 8.379 0 0 8.379 303.09 509.37 Tm 1.629 Tc [(\\\010)287(\011)]TJ /F5 1 Tf 12 0 0 12 215.25 515.01 Tm 1.581 Tc [(\010\\)552(\011)-7510(\010)30(\\)552(\011)]TJ /T33 1 Tf 6 0 0 6 300.09 506.61 Tm 2.38 Tc [(II)300(I)-880(I)]TJ /T34 1 Tf 8.379 0 0 8.379 207.21 519.69 Tm 0 Tc (M)Tj -0.1003 -0.845 TD 18.168 Tc (AA)Tj 2.9503 -0.1719 TD 2.016 Tc [(II)-13591(II)]TJ 7.2611 -0.2148 TD 1.112 Tc [(ZM)-139(Z)-974(Y)]TJ /F6 1 Tf 12 0 0 12 219.21 515.01 Tm 1.681 Tc [(YZ)-8518(Z)-28(Z)]TJ /F8 1 Tf -1.58 0 TD 12.478 Tc (QQ)Tj /T35 1 Tf 6 0 0 6 295.53 506.61 Tm 1.9 Tc [(\016\016)300(\016)-880(\016)]TJ /T36 1 Tf 8.379 0 0 8.379 225.09 511.17 Tm 17.449 Tc (\016\016)Tj 13.3192 -0.2148 TD 0 Tc (\036)Tj /F7 1 Tf 12 0 0 12 262.65 515.01 Tm (\036)Tj 18 0 0 18 276.21 512.25 Tm (\234)Tj /F3 1 Tf 12 0 0 12 414.09 515.01 Tm (.)Tj -27 -2.75 TD 0.04 Tw [(Note)4( tha)4(t)-2( for this to be)4( we)4(ll define)4(d the)4(r)-7(e)4( must )-10(be)4( )-10(positive)4( )-10(proba)4(bilit)-12(y)20( )-10(of )]TJ /F6 1 Tf 29.97 0 TD 0 Tw (I)Tj /F3 1 Tf 0.49 0 TD 0.001 Tc 0.049 Tw [( re)5(ce)5(iving)11( th)-9(e)]TJ -30.46 -1.66 TD 0 Tc [(sig)10(n)0(al )]TJ /T37 1 Tf 8.324 0 0 8.324 128.25 458.25 Tm 0 Tw (I)Tj /F6 1 Tf 11.931 0 0 11.931 122.97 462.09 Tm (Z)Tj /F3 1 Tf 12 0 0 12 133.77 462.09 Tm [( when the pla)-16(y)20(e)-6(r)3(s pla)-16(y)20( )]TJ /F6 1 Tf 11.952 0 0 11.952 245.49 462.09 Tm (A)Tj /F3 1 Tf 12 0 0 12 254.73 462.09 Tm (.)Tj /F10 1 Tf -13.72 -2.17 TD 0.1 Tw [(Def)-7(i)-2(nition 1:)]TJ /F4 1 Tf 5.47 0 TD -0.001 Tc 0.101 Tw [( A game has )]TJ /F5 1 Tf 11.97 0 0 11.97 223.29 436.05 Tm 0.403 Tc [(\010\014)-269(\011)]TJ /F8 1 Tf 0.381 0 TD 0.351 Tc (FO)Tj /F4 1 Tf 12 0 0 12 250.41 436.05 Tm 0.001 Tc 0.109 Tw [( )10(public)5( )10(information wi)9(th re)5(spe)5(c)5(t)-1( to )]TJ /F6 1 Tf 11.952 0 0 11.952 428.49 436.05 Tm 0 Tc 0 Tw (M)Tj /F4 1 Tf 12 0 0 12 441.33 436.05 Tm 0.001 Tc 0.109 Tw [( if for all ac)5(tion)]TJ -29.27 -1.67 TD -0.001 Tw [(profile)5(s a,)]TJ /F3 1 Tf 0 -2.66 TD -0.002 Tc (\(1\) )Tj ET 109.89 391.05 m 115.89 391.05 l S BT /T38 1 Tf 6 0 0 6 162.33 381.93 Tm 0 Tc 0 Tw (\012)Tj /T39 1 Tf 8.379 0 0 8.379 209.61 388.89 Tm (\012)Tj -3.738 -1.2317 TD (\012)Tj /F5 1 Tf 12 0 0 12 199.05 384.09 Tm 0.901 Tc [(\010\011)-410(\021)]TJ /T40 1 Tf 8.379 0 0 8.379 116.25 388.89 Tm 8.125 Tc (MM)Tj -0.1575 -0.845 TD 8.472 Tc (AA)Tj 5.1129 -0.3867 TD 1.011 Tc (Y9)Tj /F6 1 Tf 12 0 0 12 203.01 384.09 Tm 0 Tc (Y)Tj /F8 1 Tf -7.85 0 TD 5.708 Tc [(QQ)350(F)]TJ /T41 1 Tf 8.379 0 0 8.379 166.05 378.57 Tm 0 Tc (\211)Tj /F7 1 Tf 12 0 0 12 128.85 384.09 Tm 7.01 Tc [(wp)6052(\016)]TJ 18 0 0 18 142.41 381.45 Tm 0 Tc (\234)Tj /F3 1 Tf 12 0 0 12 90.09 352.05 Tm -0.002 Tc (\(2\) )Tj /F4 1 Tf 1.41 0 TD 0.002 Tc (if )Tj /F5 1 Tf 11.97 0 0 11.97 129.93 352.05 Tm 0.443 Tc [(\010\011)-922(\020)]TJ /T42 1 Tf 8.355 0 0 8.355 124.53 349.65 Tm 0 Tc (A)Tj /F6 1 Tf 11.97 0 0 11.97 134.13 352.05 Tm (Z)Tj /F8 1 Tf -1.3133 0 TD (Q)Tj /F7 1 Tf 2.4362 0 TD (\037)Tj /F4 1 Tf 12 0 0 12 168.69 352.05 Tm 0.001 Tc -0.001 Tw [( the)5(n)1( for all )]TJ /T43 1 Tf 8.355 0 0 8.355 235.65 356.73 Tm 0 Tc 0 Tw (\012)Tj /F5 1 Tf 11.975 0 0 11.975 271.17 352.05 Tm 0.743 Tc (\010\011)Tj /T44 1 Tf 8.355 0 0 8.355 267.57 349.65 Tm 1.261 Tc (II)Tj /F6 1 Tf 11.975 0 0 11.975 229.05 352.05 Tm 1.916 Tc [(YM)1275(Z)]TJ /F7 1 Tf 1.3228 0 TD 0 Tc (v)Tj /F4 1 Tf 12 0 0 12 291.09 352.05 Tm (, )Tj ET q 324.09 365.97 16.8 -13.44 re W* n BT /T43 1 Tf 8.355 0 0 8.355 324.09 356.73 Tm (\012)Tj ET Q BT /F5 1 Tf 11.975 0 0 11.975 313.65 352.05 Tm 1.194 Tc [(\010\\)162(\011)-1413(\010)140(\010)451(\011)972(\\)162(\011)]TJ /T44 1 Tf 8.355 0 0 8.355 305.73 356.73 Tm 7.619 Tc (MM)Tj -0.1005 -0.8474 TD 4.189 Tc [(AI)759(A)2025(I)2928(I)1736(I)]TJ /F6 1 Tf 11.975 0 0 11.975 317.49 352.05 Tm 1.305 Tc [(YZ)-2393(M)664(Z)-208(Z)]TJ /F8 1 Tf -1.5633 0 TD 5.32 Tc [(QQ)-1413(O)]TJ ET q 356.13 365.97 108.96 -18.96 re W* n BT /F7 1 Tf 11.975 0 0 11.975 356.13 352.05 Tm 6.638 Tc (b\016)Tj ET Q BT /F3 1 Tf 12 0 0 12 110.37 326.01 Tm 0.001 Tc 0.079 Tw [(Whe)5(n)1( this c)5(ondition is sa)5(tisfie)5(d)1( for )-10(some)5( )-10(positive)5( )]TJ ET q 359.25 332.97 8.76 -9.84 re W* n BT /F11 1 Tf 9.96 0 3.078 9.96 359.25 326.01 Tm 0 Tc 0 Tw (n)Tj ET Q BT 12 0 0 12 368.01 326.01 Tm 0.089 Tw [( a)5(nd \223)5(s)0(ma)5(ll\224)5( )]TJ /F8 1 Tf 13.824 0 0 13.824 435.93 326.25 Tm 0 Tc 0 Tw (F)Tj /F3 1 Tf 12 0 0 12 443.25 326.01 Tm 0.09 Tw [( we)4( sa)-16(y)20( tha)4(t)-2( the)]TJ -29.43 -1.66 TD 0.001 Tc 0.129 Tw [(g)11(a)5(m)-11(e)5( ha)5(s \223a)5(lmost public)5( me)5(ssa)5(g)11(i)-1(n)-9(g)11(.)-9(\224)5( This c)5(ondition say)21(s)0( tha)5(t)-1( most of )-10(the)5( )-10(time)5(, )-10(ea)5(c)5(h)]TJ 0 -1.67 TD 0.069 Tw [(play)21(er is fa)5(irl)-21(y)21( )-10(c)5(onfide)5(n)1(t of the)5( other pla)-15(y)21(er')11(s)0( me)5(ssag)11(e)5(; in )-10(the)5( )-10(limit )-10(c)5(a)5(s)0(e)5( )-10(of )-20(\(0,)]TJ ET q 474.21 294.09 9.96 -11.04 re W* n BT /F11 1 Tf 12.044 0 3.722 12.044 474.09 286.05 Tm 0 Tc 0 Tw (n)Tj ET Q BT 12 0 0 12 484.17 286.05 Tm 0 Tc (\)-public)Tj -32.84 -1.67 TD -0.001 Tc 0.121 Tw [(information, the two pla)-17(y)19(ers\222 m)-13(e)3(ssa)-7(g)9(e)3(s )-10(are p)-11(e)3(rf)-8(ectly)9( )-10(cor)-8(r)2(elated, so that the)-17(y)19( )-10(a)-7(r)2(e )-20(public)]TJ 0 -1.66 TD 0 Tc 0.15 Tw [(information. This condition is closel)-12(y)20( rel)-12(a)4(ted to )-10(the )-10(Mailath )-10(and )-10(Mor)-7(r)3(is )-10(definition )-10(of)]TJ 0 -1.67 TD 0 Tw (\223)Tj /F8 1 Tf 10.8 0 0 10.8 97.05 225.81 Tm (F)Tj /F3 1 Tf 12 0 0 12 104.37 226.05 Tm 0.001 Tc 0.119 Tw [(-c)5(lose)5( to public)5( monitoring)11(,)-9(\224)5( but it is we)5(a)5(k)1(er in two wa)-15(y)21(s)0(. )-10(F)7(i)-1(rst of a)5(ll, )-10(Ma)5(ila)5(th )-10(a)5(n)1(d)]TJ -1.19 -1.67 TD -0.001 Tc 0.021 Tw [(Morris suppose that ea)-7(ch pla)-17(y)19(er )]TJ /F4 1 Tf 13.11 0 TD 0 Tc 0 Tw (i)Tj /F3 1 Tf 0.28 0 TD -0.003 Tc 0.023 Tw [(\222)-10(s)-4( pri)-5(v)-3(at)-5(e si)-15(g)7(n)-3(al)-5( )]TJ /T45 1 Tf 8.348 0 0 8.348 337.77 203.61 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.963 0 0 11.963 332.49 206.01 Tm (Z)Tj /F3 1 Tf 12 0 0 12 343.29 206.01 Tm 0.001 Tc 0.029 Tw [( lie)5(s in the)5( sa)5(me)5( se)5(t a)5(s)0( do the)5( si)-11(g)11(n)1(a)5(l)-1(s)]TJ -21.1 -1.66 TD 0 Tc 0.05 Tw [(in )10(the )10(limiting)10( pubic-information game; in our setting)10( this co)-10(rresponds to )]TJ /F5 1 Tf 11.97 0 0 11.97 451.41 186.09 Tm 0.882 Tc [(\003\012)-544(\003)]TJ /T46 1 Tf 8.355 0 0 8.355 513.93 183.69 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.97 0 0 11.97 461.25 186.09 Tm 3.012 Tc (9:)Tj /F7 1 Tf 1.7144 0 TD 0 Tc (\036)Tj /F3 1 Tf 12 0 0 12 519.09 186.09 Tm (.)Tj -35.75 -1.67 TD 0.27 Tw [(Second, the)-16(y)20( suppose that in the public information )-10(limit, )-10(ever)-17(y)20( )-10(si)-12(g)10(n)0(al )-10(has )-10(strictl)-22(y)]TJ T* -0.001 Tc 0.091 Tw [(positive probabilit)-13(y)19( under )-10(ever)-18(y)19( )-10(action profile, )-10(and that the distribution of each )-10(pl)-13(a)-17(y)19(er)-8(')9(s)]TJ 0 -1.66 TD 0 Tc 0.08 Tw [(private sig)10(n)-10(als is close to this limit. These conditions )-10(impl)-12(y)30( )-10(condition )-10(\(1\) )-10(abo)-10(v)0(e, )-10(and )-20(a)]TJ 0 -1.67 TD 0.16 Tw [(strong)10(e)-6(r)3( )10(version )10(of condition \(2\), namel)-22(y)20( that )]TJ /T47 1 Tf 8.355 0 0 8.355 356.37 103.65 Tm 0 Tw (\020)Tj /F5 1 Tf 11.97 0 0 11.97 326.01 106.05 Tm [(LIM)-2988(\010)-1055(\010)-744(\011)-223(\\)-1032(\011)-1365(\021)]TJ /T48 1 Tf 8.355 0 0 8.355 370.53 110.73 Tm (M)Tj ET q 369.69 113.25 75.36 -12.24 re W* n BT 8.355 0 0 8.355 369.69 103.65 Tm 2.164 Tc [(AI)903(I)-289(I)]TJ ET Q q 382.41 116.97 64.68 -15.96 re W* n BT /F6 1 Tf 11.97 0 0 11.97 382.41 106.05 Tm 0.642 Tc [(MZ)-872(Z)]TJ ET Q BT /T49 1 Tf 8.355 0 0 8.355 343.17 103.65 Tm (F)Tj /F8 1 Tf 11.97 0 0 11.97 363.57 106.05 Tm (Q)Tj /T50 1 Tf 8.355 0 0 8.355 347.49 103.65 Tm (l)Tj /F7 1 Tf 11.97 0 0 11.97 440.49 106.05 Tm (\036)Tj /F3 1 Tf 12 0 0 12 460.41 106.05 Tm 0.16 Tw [(. Given the)]TJ -30.86 -1.67 TD 0.001 Tc 0.009 Tw [(a)5(ssumption tha)5(t)-1( )]TJ /F5 1 Tf 11.97 0 0 11.97 170.37 86.01 Tm 0.882 Tc [(\003\012)-544(\003)]TJ /T48 1 Tf 8.355 0 0 8.355 232.89 83.61 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.97 0 0 11.97 180.21 86.01 Tm 3.012 Tc (9:)Tj /F7 1 Tf 1.7144 0 TD 0 Tc (\036)Tj /F3 1 Tf 12 0 0 12 238.05 86.01 Tm -0.001 Tc 0.011 Tw [(, their conditions are equivalent to ours, but )-10(wh)-11(en )-10(there )-20(ar)-8(e)]TJ ET endstream endobj 68 0 obj << /ProcSet [/PDF /Text ] /Font << /F2 25 0 R /F3 30 0 R /F4 31 0 R /F5 34 0 R /F6 35 0 R /F7 36 0 R /F8 37 0 R /F10 52 0 R /F11 69 0 R /T25 70 0 R /T26 71 0 R /T27 72 0 R /T28 73 0 R /T29 74 0 R /T30 75 0 R /T31 76 0 R /T32 77 0 R /T33 78 0 R /T34 79 0 R /T35 80 0 R /T36 81 0 R /T37 82 0 R /T38 83 0 R /T39 84 0 R /T40 85 0 R /T41 86 0 R /T42 87 0 R /T43 88 0 R /T44 89 0 R /T45 90 0 R /T46 91 0 R /T47 92 0 R /T48 93 0 R /T49 94 0 R /T50 95 0 R >> /ExtGState << /GS1 26 0 R >> >> endobj 97 0 obj << /Length 9949 >> stream BT /F2 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g /GS1 gs 0 Tc 0 Tw (5)Tj -17.75 -3 TD 0.25 Tw [(man)-10(y)20( )10(priv)-10(ate )10(si)-12(g)10(n)0(als cor)-7(r)3(espondin)-10(g)10( to a )-10(g)10(i)-2(ven public mess)-11(ag)10(e, our )-10(condition \(2\) is)]TJ 0 -1.66 TD 0.04 Tw [(sig)10(n)0(ific)4(a)4(n)0(tl)-22(y)20( )10(w)-8(e)4(a)4(k)0(er, )10(a)4(s)-1( )10(it )10(a)4(llows )10(the)4( )10(priva)4(t)-2(e)4( )10(si)-12(g)10(n)-10(a)4(l)-2(s to diffe)4(r in how info)-10(rma)4(tive)4( the)-16(y)20( are)]TJ 0 -1.67 TD 0 Tw [(about the messag)10(e)4( the opposin)-10(g)10( pla)-16(y)20(er will send.)]TJ 3 -1.67 TD 0.001 Tc 0.199 Tw [(Note)5( )10(tha)5(t)-1( )10(our )10(c)5(ondition is e)5(a)5(s)0(ie)5(r to sa)5(tisf)-16(y)21( with c)5(o)-9(a)5(r)4(se)5( m)-11(e)5(ssag)11(e)5( ma)5(ps )]TJ /F4 1 Tf 30.13 0 TD -0.002 Tc [(m,)-12( )]TJ /F2 1 Tf 1.43 0 TD (and)Tj -34.56 -1.66 TD 0 Tc 0.27 Tw [(indeed it is vacuousl)-12(y)20( s)-11(a)4(tisfied )-10(if )]TJ /T51 1 Tf 8.355 0 0 8.355 281.13 621.69 Tm 4.606 Tc (\021\022)Tj /F5 1 Tf 11.97 0 0 11.97 286.53 624.09 Tm 0 Tc [(\305AN)-10(D)-20(\305)]TJ /F6 1 Tf -1.2532 0 TD 2.727 Tc (MM)Tj /F2 1 Tf 12 0 0 12 330.45 624.09 Tm 0.001 Tc 0.279 Tw [( a)5(r)4(e)5( e)5(q)1(u)-9(a)5(l to the)5( sa)5(me)5( c)5(onsta)5(nt; the)]TJ /F3 1 Tf -20.03 -1.67 TD 0.059 Tw [(c)5(ondition )10(will )10(ha)5(ve)5( )10(force)5( )10(whe)5(n)1( )-10(c)5(o)1(mbine)5(d)1( with the)5( a)5(ssumption tha)5(t)-1( the)5( me)5(ssag)11(e)5(s \223)5(r)4(e)5(v)-9(ea)5(l)]TJ T* -0.001 Tc 0.001 Tw [(enoug)9(h)-11(\224)3( about the )-10(action profile that )-10(g)9(e)3(n)-11(e)3(r)-8(a)3(ted the unde)-7(rl)-13(y)19(i)-3(n)-11(g)9( si)-13(g)9(n)-1(als.)]TJ 3 -1.66 TD 0.121 Tw [(Notice )10(that, )10(ex)-11(cept )10(in the trivial case o)-11(f)2( per)-8(f)2(ect info)-11(rmation, condition \(2\) rules)]TJ -3 -1.67 TD 0.001 Tc 0.109 Tw [(out the)5( possibilit)-11(y)31( tha)5(t)-1( the)5( )-10(si)-11(g)11(n)1(a)5(l)-1(s )]TJ /T52 1 Tf 8.324 0 0 8.324 268.65 540.09 Tm 1.179 Tc (\021\022)Tj /F5 1 Tf 11.931 0 0 11.931 272.85 544.05 Tm 0 Tc 0 Tw (\014)Tj /F6 1 Tf -0.7845 0 TD 0.746 Tc (ZZ)Tj /F3 1 Tf 12 0 0 12 289.29 544.05 Tm -0.001 Tc 0.121 Tw [( are independ)-11(ent conditional on )]TJ /F6 1 Tf 11.952 0 0 11.952 451.53 544.05 Tm 0 Tc 0 Tw (A)Tj /F3 1 Tf 12 0 0 12 460.77 544.05 Tm -0.002 Tc 0.122 Tw [(. )-10(I)21(n)-2( essen)-12(ce,)]TJ -30.89 -1.67 TD -0.001 Tc 0.071 Tw [(condition \(2\) requir)-8(e)3(s that if one pla)-17(y)19(e)-7(r)2( r)-8(eceives )-10(a )-10(sig)9(n)-11(al )-10(that )-10(was )-10(unlikel)-23(y)19( )-10(conditional)]TJ 0 -1.66 TD 0 Tc (on )Tj /F6 1 Tf 11.952 0 0 11.952 106.29 504.09 Tm 0 Tw (A)Tj /F3 1 Tf 12 0 0 12 115.53 504.09 Tm -0.001 Tc 0.051 Tw [(, )10(it )10(is )10(likel)-13(y)29( )10(that )10(the othe)-7(r pla)-17(y)19(e)-7(r)2( re)-7(ceive the )-10(corr)-8(esponding)9( )-10(unlikel)-13(y)19( si)-13(g)9(n)-1(al \226 that is,)]TJ -2.12 -1.67 TD -0.003 Tc 0.003 Tw [(t)-5(h)-3(at)-5( t)-5(h)-3(e errors )-10(are )-10(corr)-10(el)-5(at)-5(ed.)]TJ /F2 1 Tf 8.04 0 0 8.04 228.33 489.57 Tm 0 Tc 0 Tw (6)Tj /F3 1 Tf 12 0 0 12 126.09 464.01 Tm -0.006 Tc 0.006 Tw [(Fo)-6(r a )-10(gi)-8(v)-16(e)-2(n)-6( )]TJ /F5 1 Tf 11.963 0 0 11.963 190.65 464.01 Tm 0 Tc 0 Tw (\014)Tj /F6 1 Tf -0.5116 0 TD 0.362 Tc (AM)Tj /F3 1 Tf 12 0 0 12 207.81 464.01 Tm -0.001 Tc 0.001 Tw [( we can conside)-7(r)2( )]TJ /F5 1 Tf 11.97 0 0 11.97 307.77 464.01 Tm 0.253 Tc [(\010\\)-749(\012)251(\011)]TJ /T53 1 Tf 8.355 0 0 8.355 299.73 468.69 Tm 0 Tc 0 Tw (M)Tj -0.1005 -0.8474 TD (A)Tj ET q 1 i 320.13 474.93 22.92 -15.96 re W* n BT /F6 1 Tf 11.97 0 0 11.97 320.13 464.01 Tm (9)Tj ET Q BT /F8 1 Tf 11.97 0 0 11.97 292.77 464.01 Tm (Q)Tj /F9 1 Tf 1.6241 0 TD (<)Tj /F3 1 Tf 12 0 0 12 343.05 464.01 Tm -0.001 Tc 0.001 Tw [( as )-10(a )-10(row )-10(ve)-7(ctor. )-10(F)5(o)-11(r )-10(pla)-17(y)19(e)-7(r)2( )]TJ /F6 1 Tf 11.37 0 TD 0 Tc 0 Tw (I)Tj /F3 1 Tf 0.49 0 TD -0.004 Tc 0.014 Tw [( we can)]TJ -32.94 -1.66 TD 0.001 Tc 0.169 Tw [(c)5(onstruc)5(t a)5( ma)5(trix)-9( )]TJ /T54 1 Tf 8.379 0 0 8.379 203.49 448.77 Tm 0 Tc 0 Tw (\014)Tj /T55 1 Tf -0.845 0 TD 0.291 Tc (MI)Tj -0.0286 -0.845 TD 0 Tc (A)Tj /F7 1 Tf 12 0 0 12 187.53 444.09 Tm (1)Tj /F3 1 Tf 1.94 0 TD -0.001 Tc 0.181 Tw [( )10(b)-11(y)19( )10(stac)-7(king)9( th)-11(e row ve)-7(ctors co)-11(rrespondin)-11(g)9( to )]TJ /F5 1 Tf 12.028 0 0 12.028 450.69 444.09 Tm 0.718 Tc [(\010\014)-678(\011)]TJ /T56 1 Tf 8.391 0 0 8.391 460.53 440.25 Tm 2.041 Tc (II)Tj /F6 1 Tf 12.028 0 0 12.028 454.29 444.09 Tm 0.616 Tc (AA)Tj /T57 1 Tf 8.391 0 0 8.391 474.09 440.25 Tm 0 Tc 0 Tw (\016)Tj /F9 1 Tf 12.028 0 0 12.028 455.85 444.45 Tm (\004)Tj /F3 1 Tf 12 0 0 12 489.81 444.09 Tm -0.002 Tc 0.182 Tw [( as )]TJ /T58 1 Tf 8.355 0 0 8.355 517.05 440.25 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 11.97 0 0 11.97 510.81 444.09 Tm (A)Tj /F9 1 Tf 0.1303 0.0301 TD (\004)Tj /F3 1 Tf 12 0 0 12 90.09 424.05 Tm -0.002 Tc 0.042 Tw [(ran)-12(g)8(es ove)-8(r )]TJ /T59 1 Tf 8.391 0 0 8.391 158.25 420.21 Tm 0 Tc 0 Tw (I)Tj /F6 1 Tf 12.028 0 0 12.028 150.93 424.05 Tm (!)Tj /F3 1 Tf 12 0 0 12 163.65 424.05 Tm -0.001 Tc 0.051 Tw [(. )10( )10(W)-7(e)3( )10(can )10(further sta)-7(c)3(k the two matric)-7(es cor)-8(r)2(espondin)-11(g)9( to the two pla)-17(y)19(e)-7(r)2(s)]TJ -6.13 -1.67 TD 0.002 Tc 0.048 Tw [(to g)12(e)6(t a)6( )]TJ /F7 1 Tf 12.019 0 0 11.222 131.01 404.13 Tm 5.483 Tc (\011\012)Tj /T60 1 Tf 8.355 0 0 8.355 155.61 401.61 Tm 4.203 Tc (\021\022)Tj /F5 1 Tf 11.97 0 0 11.97 136.77 404.01 Tm 2.446 Tc [(\003\003)-291(\003)1293(\012)]TJ /F6 1 Tf 0.9524 0 TD 2.536 Tc [(!!)-161(9)]TJ /F7 1 Tf 1.3033 0 TD 2.877 Tc (\014q)Tj /F3 1 Tf 12 0 0 12 250.17 404.01 Tm 0.001 Tc 0.049 Tw [( ma)5(trix)-9( )]TJ /T61 1 Tf 8.355 0 0 8.355 299.25 408.69 Tm 0 Tc 0 Tw (M)Tj -0.0287 -0.8474 TD (A)Tj /F7 1 Tf 11.97 0 0 11.97 290.37 404.01 Tm (1)Tj /F3 1 Tf 12 0 0 12 308.73 404.01 Tm 0.05 Tw [(. Notic)4(e)4( tha)4(t)-2( this ma)4(trix)-10( ha)4(s two )-10(rows )-10(\(both)]TJ -18.22 -1.66 TD -0.001 Tc 0.001 Tw [(correspondin)-11(g)9( to )]TJ /F6 1 Tf 11.952 0 0 11.952 174.81 384.09 Tm 0 Tc 0 Tw (A)Tj /F3 1 Tf 12 0 0 12 184.05 384.09 Tm -0.003 Tc 0.003 Tw [(\) t)-5(h)-3(at)-5( are i)-5(d)-3(ent)-5(i)-5(c)-9(al)-5(.)]TJ /F10 1 Tf -7.83 -2.17 TD 0 Tc 0.02 Tw [(Def)-7(i)-2(nition 2: )]TJ /F4 1 Tf 5.94 0 TD -0.001 Tc 0.031 Tw (A game has )Tj /F3 1 Tf 5 0 TD 0.001 Tc 0.029 Tw [(pure)5(-)4(stra)5(teg)-9(y)21( p)-9(a)5(irwise)5( full ra)5(nk)]TJ /F4 1 Tf 12.66 0 TD [( with re)5(spe)5(c)5(t)-1( to )]TJ /F6 1 Tf 11.952 0 0 11.952 452.61 358.05 Tm 0 Tc 0 Tw (M)Tj /F4 1 Tf 12 0 0 12 465.45 358.05 Tm -0.002 Tc 0.032 Tw [( i)-4(f)-4( f)-4(o)-2(r every)]TJ -31.28 -1.67 TD 0.001 Tc -0.001 Tw [(pure)5( profile)5( )]TJ /F3 1 Tf 5.25 0 TD 0 Tc 0 Tw ( )Tj /F4 1 Tf 0.25 0 TD -0.001 Tc 0.001 Tw (a the rank of )Tj /T61 1 Tf 8.355 0 0 8.355 233.61 342.69 Tm 0 Tc 0 Tw (M)Tj -0.0287 -0.8474 TD (A)Tj /F7 1 Tf 11.97 0 0 11.97 224.73 338.01 Tm (1)Tj /F4 1 Tf 12 0 0 12 243.09 338.01 Tm 0.002 Tc (is )Tj /F7 1 Tf 11.922 0 0 13.965 254.97 337.65 Tm 5.44 Tc (\011\012)Tj /T62 1 Tf 8.391 0 0 8.391 278.97 334.05 Tm 4.112 Tc (\021\022)Tj /F5 1 Tf 12.024 0 0 12.024 260.61 338.01 Tm 2.362 Tc [(\003\003)-409(\021)]TJ /F6 1 Tf 0.9282 0 TD 2.462 Tc (!!)Tj /F7 1 Tf 1.2675 0 TD 2.881 Tc (\014\016)Tj /F4 1 Tf 12 0 0 12 349.17 338.01 Tm 0 Tc (.)Tj /F3 1 Tf -21.59 -2.16 TD -0.001 Tc 0.011 Tw [(This )10(condition )10(is )10(never )10(satisfied )10(in )10(games )10(such as Gre)-7(e)3(n and Porte)-7(r)2( [)-8(1984])-8(, where the two)]TJ 0 -1.67 TD 0 Tc 0.04 Tw [(pla)-6(y)20(e)-6(r)3(s hav)-10(e)4( the same s)-11(e)4(ts of fe)-6(asible actions, and the distribution )-10(of )-10(si)-12(g)10(n)0(als )-10(satisfies )-10(the)]TJ T* 0.001 Tc 0.259 Tw [(s)-10(y)21(mme)5(tr)-16(y)21( c)5(ondition tha)5(t)-1( )]TJ /T63 1 Tf 8.379 0 0 8.379 227.73 269.73 Tm 0.626 Tc [(\010\014)-173(\007)643(\011)-2305(\010)-157(\007)643(\014)-73(\011)]TJ /T64 1 Tf 0.401 0 TD 0.264 Tc [(BB)-3753(B)-330(B)]TJ /F8 1 Tf 12 0 0 12 221.49 272.01 Tm 3.328 Tc (QQ)Tj /F7 1 Tf 2.77 0 TD 0 Tc 0 Tw (\036)Tj /F4 1 Tf 3.67 0 TD (, )Tj /F3 1 Tf 0.76 0 TD 0.26 Tw [(but it is sa)4(tisfie)4(d)0( for a)4( se)4(t of )-10(proba)4(bilit)-12(y)]TJ -18.15 -1.66 TD -0.002 Tc [(m)-4(easures )]TJ /T65 1 Tf 8.348 0 0 8.348 145.53 249.69 Tm 0 Tc 0 Tw (A)Tj /F8 1 Tf 11.963 0 0 11.963 139.41 252.09 Tm (Q)Tj /F3 1 Tf 12 0 0 12 152.73 252.09 Tm -0.001 Tc 0.001 Tw [( of full )-10(L)10(e)3(bes)-12(g)9(ue m)-13(easur)-8(e.)]TJ -5.22 -7.97 TD 0 Tc 0 Tw ( )Tj ET 1 i 90.09 159.57 143.88 -0.48 re f BT /F2 1 Tf 8.04 0 0 8.04 90.09 147.21 Tm (6)Tj /F3 1 Tf 12 0 0 12 94.17 141.69 Tm 0.03 Tw [( )10(Matsushima )10([)-7(1991])-7( )10(prove)14(d )10(that pay)20(o)0(ffs of )-10(equilibria with truthful, incentive comp)-10(atible)]TJ -0.34 -1.15 TD -0.001 Tc 0.131 Tw [(revelation of the si)-13(g)9(n)-1(als e)-7(v)-1(er)-18(y)19( p)-11(e)3(riod ar)-8(e bounded a)-7(w)1(a)-17(y)19( )-10(from ef)-8(ficienc)-17(y)19( )-10(in )-10(two-pla)-17(y)19(e)-7(r)]TJ T* 0 Tc 0.13 Tw [(g)10(a)4(m)-12(e)4(s with independent si)-12(g)10(n)0(als; subsequent wo)-10(rk b)-20(y)20( )-10(Compte )-10([)-7(1998])-7( )-10(and )-10(Kandori )-10(and)]TJ T* 0.29 Tw [(Matsushima [)-7(1998])-7( )10(show that it is possib)10(l)-2(e to )-10(work )-10(with )-10(independent )-10(sig)10(n)-10(als )-10(b)-10(y)]TJ T* 0 Tw [(considerin)-10(g)10( strate)-6(g)10(i)-2(es that onl)-22(y)20( r)-7(e)4(port truthfull)-22(y)20( periodic)-6(a)4(ll)-12(y)20(.)]TJ ET endstream endobj 98 0 obj << /ProcSet [/PDF /Text ] /Font << /F2 25 0 R /F3 30 0 R /F4 31 0 R /F5 34 0 R /F6 35 0 R /F7 36 0 R /F8 37 0 R /F9 51 0 R /F10 52 0 R /T51 99 0 R /T52 100 0 R /T53 101 0 R /T54 102 0 R /T55 103 0 R /T56 104 0 R /T57 105 0 R /T58 106 0 R /T59 107 0 R /T60 108 0 R /T61 109 0 R /T62 110 0 R /T63 111 0 R /T64 112 0 R /T65 113 0 R >> /ExtGState << /GS1 26 0 R >> >> endobj 114 0 obj << /Length 14340 >> stream BT /F2 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g /GS1 gs 0 Tc 0 Tw (6)Tj /F1 1 Tf -17.75 -3 TD 0.001 Tc 0.001 Tw [(4. The Nash Threats Folk Th)12(eorem)]TJ /F2 1 Tf 3 -1.91 TD -0.011 Tc [(Le)-7(t)-13( )]TJ /F5 1 Tf 11.963 0 0 11.963 155.73 681.09 Tm 0 Tc 0 Tw (\012)Tj /F6 1 Tf -0.7624 0 TD (V)Tj /F2 1 Tf 12 0 0 12 163.53 681.09 Tm -0.001 Tc 0.051 Tw [( )10(be )10(a )10(static N)-9(a)3(sh pa)-17(y)19(o)-1(f)-8(f)2( vecto)-11(r)2(. W)-7(e)3( ma)-7(y)19( )-10(convenientl)-23(y)19( norm)-13(a)3(liz)-7(e )]TJ /F5 1 Tf 11.963 0 0 11.963 488.13 681.09 Tm 1.447 Tc (\012\020)Tj /F6 1 Tf -0.5015 0 TD 0 Tc 0 Tw (V)Tj /F7 1 Tf 1.3141 0 TD (\036)Tj /F2 1 Tf 12 0 0 12 519.09 681.09 Tm (.)Tj -35.75 -1.67 TD 0.001 Tc -0.001 Tw [(F)7(i)-1(x)-9( a)5( se)5(que)5(nc)5(e)5( o)-9(f)4( )-10(g)11(a)5(me)5(s with c)5(o)1(mmon)]TJ /F5 1 Tf 11.97 0 0 11.97 286.65 661.05 Tm 0.763 Tc [(\014\014)-100(\012)761(\014)]TJ /F6 1 Tf -0.6717 0 TD 0.291 Tc [(!:)-30(9)-756(G)]TJ /F2 1 Tf 12 0 0 12 332.37 661.05 Tm 0.001 Tc [(, a)5(nd with sig)11(n)1(a)5(l)-1( prob)-9(a)5(b)1(ilitie)5(s )]TJ /T66 1 Tf 8.348 0 0 8.348 486.33 665.73 Tm 0 Tc 0 Tw (N)Tj /F8 1 Tf 11.963 0 0 11.963 479.37 661.05 Tm (Q)Tj /F2 1 Tf 12 0 0 12 493.65 661.05 Tm (.)Tj /F10 1 Tf -33.63 -2.17 TD -0.003 Tc [(T)-6(h)-7(eore)-9(m)]TJ /F4 1 Tf 3.88 0 TD -0.001 Tc 0.011 Tw [(: Suppose th)-11(ere is a message profile )]TJ ET q 1 i 314.97 642.93 12.84 -9.96 re W* n BT /F6 1 Tf 11.952 0 0 11.952 314.97 635.01 Tm 0 Tc 0 Tw (M)Tj ET Q BT 12 0 0 12 327.81 635.01 Tm 0 Tc 0.01 Tw [( and a )]TJ /F2 1 Tf 10 0 0 10 377.97 635.01 Tm 0 Tw (0)Tj ET q 1 i 361.53 644.01 20.04 -11.88 re W* n BT /F11 1 Tf 10 0 3.09 10 361.53 635.01 Tm (n)Tj ET Q BT /F11 1 Tf 10 0 0 10 370.41 635.01 Tm (>)Tj /F4 1 Tf 12 0 0 12 385.29 635.01 Tm -0.001 Tc 0.021 Tw [( such t)-3(hat)-3( f)-3(o)-1(r each )]TJ /F6 1 Tf 11.952 0 0 11.952 479.97 635.01 Tm 0 Tc 0 Tw (N)Tj /F4 1 Tf 12 0 0 12 489.93 635.01 Tm 0.02 Tw (, game)Tj -33.32 -1.66 TD (n has )Tj /F5 1 Tf 11.97 0 0 11.97 120.21 615.09 Tm 0.934 Tc [(\010\014)282(\011)]TJ /T67 1 Tf 8.355 0 0 8.355 130.29 619.77 Tm 0 Tc 0 Tw (N)Tj /F8 1 Tf 11.97 0 0 11.97 124.77 615.09 Tm 0.872 Tc (FO)Tj /F4 1 Tf 12 0 0 12 153.33 615.09 Tm 0.001 Tc 0.029 Tw [( public)5( information wi)9(th re)5(spe)5(c)5(t)-1( to )]TJ /F6 1 Tf 11.952 0 0 11.952 325.89 615.09 Tm 0 Tc 0 Tw (M)Tj /F4 1 Tf 12 0 0 12 338.73 615.09 Tm 0.001 Tc 0.029 Tw (, that )Tj /F5 1 Tf 11.963 0 0 11.963 401.37 615.09 Tm 0 Tc 0 Tw (\020)Tj /T68 1 Tf 8.348 0 0 8.348 374.49 619.77 Tm (N)Tj /F8 1 Tf 11.963 0 0 11.963 368.97 615.09 Tm (F)Tj /F7 1 Tf 1.3442 0 TD (l)Tj /F4 1 Tf 12 0 0 12 409.29 615.09 Tm -0.001 Tc 0.031 Tw [(, tha)9(t)-3( these games have)]TJ -26.6 -1.67 TD 0 Tc 0.03 Tw [(common diagonal probabilities )]TJ /F5 1 Tf 11.97 0 0 11.97 266.25 595.05 Tm 0.002 Tc [(\010)-441(\\)-1010(\012\011)-2657(\010)-451(\\)-1000(\012\011)]TJ /T69 1 Tf 8.355 0 0 8.355 253.65 599.73 Tm -0.007 Tc [(MN)-7312(M)]TJ -0.1005 -0.8473 TD 8.167 Tc (AA)Tj /F6 1 Tf 11.97 0 0 11.97 281.01 595.05 Tm 4.936 Tc (99)Tj /F8 1 Tf -2.8673 0 TD 5.493 Tc (QQ)Tj /F7 1 Tf 1.955 0 TD 2.707 Tc [(\270\036)790(\270)]TJ /F4 1 Tf 12 0 0 12 371.97 595.05 Tm 0 Tc 0.04 Tw (, and that )Tj /F5 1 Tf 11.97 0 0 11.97 438.69 595.05 Tm 0.423 Tc [(\010\\)-579(\012)421(\011)]TJ /T70 1 Tf 8.355 0 0 8.355 430.65 599.73 Tm 0 Tc 0 Tw (M)Tj -0.1005 -0.8473 TD (A)Tj /F6 1 Tf 11.97 0 0 11.97 453.09 595.05 Tm (9)Tj /F8 1 Tf -2.4562 0 TD (Q)Tj /F7 1 Tf 1.5539 0 TD (\270)Tj /F4 1 Tf 12 0 0 12 476.01 595.05 Tm -0.001 Tc 0.041 Tw [(has pure-)]TJ -32.16 -1.67 TD 0.001 Tc 0.109 Tw [(strate)5(gy)5( pairwise)5( full rank)5( with re)5(spe)5(c)5(t)-1( to m. The)5(n)1( the)5(r)0(e)5( is a se)5(que)5(nc)5(e)5( )]TJ /F5 1 Tf 11.97 0 0 11.97 487.29 575.01 Tm 0 Tc 0 Tw (\020)Tj /T71 1 Tf 8.355 0 0 8.355 460.29 579.69 Tm (N)Tj /F8 1 Tf 11.97 0 0 11.97 453.45 575.01 Tm (H)Tj /F7 1 Tf 1.4637 0 TD (l)Tj /F4 1 Tf 12 0 0 12 495.69 575.01 Tm -0.002 Tc 0.122 Tw [( such)]TJ -33.8 -1.66 TD -0.001 Tc 0.001 Tw [(t)-3(hat)-3( f)-3(o)-1(r any f)-3(e)3(asi)-3(b)-1(l)-3(e)3( vect)-3(or of)-3( payof)-3(f)-3(s)-2( )]TJ /F5 1 Tf 11.963 0 0 11.963 296.61 555.09 Tm 0 Tc 0 Tw (\020)Tj /F6 1 Tf -1.936 0 TD (V)Tj /F7 1 Tf 0.8225 0 TD (\037)Tj /F4 1 Tf 12 0 0 12 304.29 555.09 Tm 0.001 Tc 0.009 Tw [( in the)5( inte)5(rior of the)5( fe)5(asible)5( se)5(t the)5(r)0(e)5( e)5(x)5(i)-1(sts)]TJ /F5 1 Tf 11.931 0 0 11.931 97.17 535.05 Tm 1.342 Tc (\012\021)Tj /F8 1 Tf -0.4727 0 TD 0 Tc 0 Tw (E)Tj /F7 1 Tf 1.2773 0 TD (\035)Tj /F4 1 Tf 12 0 0 12 126.09 535.05 Tm 0.08 Tw [( such that for any )]TJ /F6 1 Tf 11.952 0 0 11.952 218.97 535.05 Tm 0 Tw (N)Tj /F4 1 Tf 12 0 0 12 228.93 535.05 Tm 0.001 Tc 0.079 Tw (and all )Tj /F5 1 Tf 5.97 0 TD 0 Tc 0 Tw (\012)Tj /F8 1 Tf -2.63 0 TD 1.441 Tc (EE)Tj /F7 1 Tf 0.81 0 TD 0 Tc (p)Tj /F4 1 Tf 2.49 0 TD 0.001 Tc 0.079 Tw [( )10(the)5(r)0(e)5( is a pe)5(rfe)5(c)5(t)-1( public)5( e)5(quilibrium in the)]TJ -18.21 -1.67 TD -0.002 Tc (game )Tj /F6 1 Tf 11.952 0 0 11.952 120.21 515.01 Tm 0 Tc 0 Tw (N)Tj /F4 1 Tf 12 0 0 12 130.17 515.01 Tm 0.001 Tc -0.001 Tw [(with pay)5(offs )]TJ /T72 1 Tf 8.348 0 0 8.348 198.69 519.69 Tm 0 Tc 0 Tw (N)Tj /F6 1 Tf 11.963 0 0 11.963 192.57 515.01 Tm (V)Tj /F4 1 Tf 12 0 0 12 206.49 515.01 Tm 0.001 Tc [(satisfy)5(ing )]TJ ET 0 G 2 J 0 j 0.588 w 10 M []0 d 1 i 259.53 523.77 m 259.53 512.13 l 257.73 523.77 m 257.73 512.13 l 298.41 523.77 m 298.41 512.13 l 296.61 523.77 m 296.61 512.13 l S BT /T73 1 Tf 8.355 0 0 8.355 267.45 519.69 Tm 6.099 Tc (NN)Tj /F6 1 Tf 11.97 0 0 11.97 261.21 515.01 Tm 1.785 Tc (VV)Tj ET q 316.29 525.93 14.16 -15.96 re W* n BT /F8 1 Tf 11.97 0 0 11.97 316.29 515.01 Tm 0 Tc (H)Tj ET Q BT /F7 1 Tf 11.97 0 0 11.97 276.69 515.01 Tm 1.414 Tc (\016\035)Tj /F4 1 Tf 12 0 0 12 330.45 515.01 Tm 0 Tc (.)Tj -20.03 -3.83 TD (Proof)Tj /F2 1 Tf 2.28 0 TD -0.001 Tc 0.071 Tw [(: )10(To )10(beg)9(i)-3(n, we suppos)-12(e that pla)-17(y)19(e)-7(r)2(s use the )-10(g)9(i)-3(ven mess)-12(a)-7(g)9(e pro)-11(f)2(ile )]TJ /F4 1 Tf 27.28 0 TD -0.002 Tc (m,)Tj /F2 1 Tf 0.97 0 TD -0.001 Tc [( and )-10(consider)]TJ -30.53 -1.67 TD 0.011 Tw [(public equilibria of the )-10(g)9(a)3(me whos)-12(e public sig)9(n)-11(als ar)-8(e )-10(the )-10(announ)-11(cements.)]TJ /F4 1 Tf 29.91 0 TD 0 Tc 0 Tw ( )Tj /F2 1 Tf 0.27 0 TD 0.006 Tc 0.014 Tw [( Wh)6(e)10(n)6( p)6(l)4(a)-10(y)26(er)9(s)]TJ -30.18 -1.66 TD -0.002 Tc (use )Tj /F4 1 Tf 1.61 0 TD (m )Tj /F2 1 Tf 1 0 TD 0.042 Tw [(and )10(t)-4(h)-2(ei)-4(r )10(si)-14(g)8(n)-2(al)-4(s )10(a)-8(r)1(e )10(hi)-14(g)8(h)-2(l)-24(y)18( )10(cor)-9(r)1(el)-4(at)-4(ed, )10(t)-4(h)-12(e)-18(y)18( )10(ar)-9(e l)-4(i)-4(k)-2(el)-14(y)18( )-10(\(but)-4( not)-4( cert)-14(a)2(i)-4(n)-2(\) t)-4(o)-2( m)-4(a)2(ke t)-4(h)-2(e)]TJ -2.61 -1.67 TD 0 Tc 0.05 Tw [(same announc)-6(ements. )-20(L)11(e)4(t )]TJ /F7 1 Tf 11.963 0 0 11.963 224.73 409.05 Tm 0 Tw (\()Tj /F2 1 Tf 12 0 0 12 234.09 409.05 Tm 0.06 Tw [( be an aux)-10(iliar)-7(y)20( )-10(g)10(a)4(m)-12(e)4( of public information without public)]TJ -12 -1.67 TD -0.001 Tc 0.241 Tw [(randomiz)-7(ations, )10(with )10(the )10(same pa)-7(y)19(o)-11(ff fun)-11(c)3(tions as in the ori)-13(g)9(inal )-10(g)9(a)3(me, )-10(and whose)]TJ 0 -1.66 TD 0 Tc 0.12 Tw [(distribution over public sig)10(n)0(als is the conditional distribution on )]TJ /F5 1 Tf 11.963 0 0 11.963 427.65 369.09 Tm 0 Tw (\012)Tj /F6 1 Tf -1.1636 0 TD (9)Tj /F2 1 Tf 12 0 0 12 435.21 369.09 Tm -0.001 Tc 0.131 Tw [( g)9(e)3(ne)-7(rated b)-21(y)19( th)-11(e)]TJ -28.76 -1.67 TD 0.001 Tc -0.001 Tw [(c)5(o)1(mmon dia)5(g)11(on)-9(a)5(l)-1( proba)5(bilitie)5(s.)]TJ 8.04 0 0 8.04 242.37 354.57 Tm 0 Tc 0 Tw (7)Tj 12 0 0 12 126.09 329.01 Tm -0.001 Tc 0.111 Tw [(Using)9( the )-10(ar)-8(g)9(u)-1(ments from )-10(F)5(udenb)-11(er)-8(g)9(,)-1( )-10(L)10(e)3(vine, )-10(and Maskin [)-8(1994])-8( and Mc)-7(L)10(ean,)]TJ -3 -1.66 TD 0.121 Tw [(Obara and )10(Postlewaite [)-8(2003])-8(, one can show that for )-10(an)-21(y)19( )]TJ /F5 1 Tf 11.931 0 0 11.931 382.05 309.45 Tm 0 Tc 0 Tw (e)Tj 1.8506 -0.0302 TD (\020)Tj /F6 1 Tf -1.9411 0 TD (V)Tj /F7 1 Tf 0.8247 0 TD (\037)Tj /F2 1 Tf 12 0 0 12 411.81 309.09 Tm 0.001 Tc 0.119 Tw [( stric)5(t)-1(l)-11(y)31( interior to the)]TJ -26.81 -1.67 TD 0.069 Tw [(fe)5(a)5(s)0(ible)5( se)5(t there)5( is a)5(n)1( )]TJ /F8 1 Tf 11.963 0 0 11.963 204.93 289.05 Tm 0 Tc 0 Tw (I)Tj /F2 1 Tf 12 0 0 12 213.21 289.05 Tm -0.002 Tc 0.072 Tw [( such t)-4(h)-2(at)-4( for an)-22(y)18( i)-4(n)-2(t)-4(e)-8(ri)-4(or )]TJ /F5 1 Tf 12.88 0.03 TD 0 Tc 0 Tw (e)Tj ET q 344.01 300.09 30.84 -15 re W* n BT /F6 1 Tf 12 0 0 12 344.01 289.05 Tm 1.419 Tc (VV)Tj ET Q BT /F7 1 Tf 12 0 0 12 354.09 289.05 Tm (p)Tj /F2 1 Tf 1.73 0 TD -0.004 Tc 0.074 Tw [( t)-6(h)-4(ere ex)-14(i)-6(s)-5(t)-6(s)-5( )]TJ /F5 1 Tf 12.028 0 0 12.028 440.25 292.29 Tm 0 Tc 0 Tw (e)Tj 1.7659 -0.2694 TD (\021)Tj /F8 1 Tf -1.8557 0 TD (E)Tj /F7 1 Tf 0.8281 0 TD (\035)Tj /F2 1 Tf 12 0 0 12 468.69 289.05 Tm -0.002 Tc 0.092 Tw (, a )Tj /F5 1 Tf 11.931 0 0 11.931 514.05 289.05 Tm 0 Tc 0 Tw (\020)Tj /F6 1 Tf -2.3233 0 TD (+)Tj /F7 1 Tf 1.217 0 TD (\037)Tj /F2 1 Tf 12 0 0 12 90.09 269.01 Tm -0.001 Tc 0.001 Tw [(and a set of p)-11(a)-17(y)19(o)-1(ffs )]TJ /F4 1 Tf 8.07 0 TD (V )Tj /F2 1 Tf 0.86 0 TD 0.001 Tc (with )Tj /F6 1 Tf 11.931 0 0 11.931 222.81 269.01 Tm 1.188 Tc (V6)Tj /F7 1 Tf 0.8448 0 TD 0 Tc 0 Tw (\211)Tj /F2 1 Tf 12 0 0 12 255.69 269.01 Tm -0.001 Tc 0.001 Tw (, and )Tj ET q 313.89 279.93 10.08 -15.96 re W* n BT /F5 1 Tf 11.97 0 0 11.97 313.89 269.37 Tm 0 Tc 0 Tw (e)Tj ET Q BT /F5 1 Tf 11.97 0 0 11.97 294.21 269.01 Tm 0 Tc 0 Tw (\007)Tj /T74 1 Tf 8.355 0 0 8.355 288.45 266.61 Tm 3.272 Tc (II)Tj /F6 1 Tf 11.97 0 0 11.97 282.93 269.01 Tm 2.045 Tc (VV)Tj /F7 1 Tf 1.4437 0 TD 0 Tc (p)Tj /F2 1 Tf 12 0 0 12 323.97 269.01 Tm -0.001 Tc 0.001 Tw ( for all )Tj /F4 1 Tf 2.91 0 TD 0.002 Tc (i )Tj /F2 1 Tf 0.53 0 TD 0 Tc 0.01 Tw (and all )Tj /F5 1 Tf 11.931 0 0 11.931 409.53 269.01 Tm 0 Tw (\007)Tj /F6 1 Tf -0.6538 0 TD 1.5 Tc (V6)Tj /F7 1 Tf 1.1566 0 TD 0 Tc (\211)Tj /F2 1 Tf 12 0 0 12 437.61 269.01 Tm -0.002 Tc 0.012 Tw [(, such t)-4(h)-12(at)-4(, for al)-4(l)]TJ ET 92.61 259.29 m 98.61 259.29 l S BT /F5 1 Tf 12.028 0 0 12.028 116.85 252.33 Tm 0 Tc 0 Tw (e)Tj /F8 1 Tf -2.1051 -0.2694 TD 1.566 Tc (EE)Tj /F7 1 Tf 0.9278 0 TD 0 Tc (\037)Tj /F2 1 Tf 12 0 0 12 124.05 249.09 Tm -0.002 Tc 0.052 Tw [( and ever)-19(y)18( )]TJ /F5 1 Tf 11.931 0 0 11.931 187.65 249.09 Tm 0 Tc 0 Tw (\007)Tj /F6 1 Tf -0.6538 0 TD 1.5 Tc (V6)Tj /F7 1 Tf 1.1566 0 TD 0 Tc (\211)Tj /F2 1 Tf 12 0 0 12 215.73 249.09 Tm 0.001 Tc 0.049 Tw [(, the)5(r)4(e)5( is a)5( p)-9(e)5(rfec)5(t public)5( e)5(quilibrium )]TJ /T75 1 Tf 8.355 0 0 8.355 409.53 253.77 Tm 0 Tc 0 Tw (\012)Tj /F8 1 Tf 11.97 0 0 11.97 402.21 249.09 Tm (T)Tj /F2 1 Tf 12 0 0 12 415.77 249.09 Tm 0.06 Tw [(with pay)20(o)0(ffs )]TJ /F5 1 Tf 11.963 0 0 11.963 489.33 249.09 Tm 0 Tw (\007)Tj /F6 1 Tf -0.652 0 TD (V)Tj /F2 1 Tf 12 0 0 12 493.41 249.09 Tm -0.001 Tc 0.061 Tw (, such)Tj -33.61 -1.67 TD 0.001 Tc [(tha)5(t)-1(:)]TJ 8.04 0 0 8.04 111.45 234.57 Tm 0 Tc 0 Tw (8)Tj 12 0 0 12 126.09 189.09 Tm -0.004 Tc (a\))Tj /F12 1 Tf 0.77 0 TD 0 Tc ( )Tj /F2 1 Tf 0.73 0 TD -0.001 Tc 0.001 Tw [(the continuation pa)-17(y)19(o)-1(ffs )]TJ /F5 1 Tf 11.97 0 0 11.97 273.09 189.09 Tm 0.473 Tc (\010\011)Tj /F6 1 Tf -0.6918 0 TD 0.363 Tc (WY)Tj /F2 1 Tf 12 0 0 12 289.77 189.09 Tm 0.001 Tc -0.001 Tw [( lie)5( in )]TJ /F4 1 Tf 2.53 0 TD -0.001 Tc (V )Tj /F2 1 Tf 0.86 0 TD 0.001 Tw (for all )Tj /T76 1 Tf 8.355 0 0 8.355 394.65 193.77 Tm 0 Tc 0 Tw (\012)Tj ET q 363.33 202.89 37.08 -18.84 re W* n BT /F6 1 Tf 11.975 0 0 11.975 363.33 189.09 Tm 1.205 Tc (Y9)Tj ET Q BT /F7 1 Tf 11.975 0 0 11.975 373.77 189.09 Tm (\211)Tj /F2 1 Tf 12 0 0 12 400.41 189.09 Tm (,)Tj -22.86 -1.67 TD (b\))Tj /F12 1 Tf 0.83 0 TD ( )Tj /F2 1 Tf 0.67 0 TD ( )Tj ET 149.37 178.05 m 149.37 166.05 l 216.93 178.05 m 216.93 166.05 l 269.25 179.25 m 275.25 179.25 l S BT /F5 1 Tf 12 0 0 12 159.57 169.05 Tm 0.471 Tc [(\010\011)-1340(\010)-160(\007)471(\011)-1970(\010)550(\021)-1289(\011)]TJ /F6 1 Tf -0.69 0 TD 0.36 Tc [(WY)-1191(WY)-2001(+)]TJ /F8 1 Tf 9.75 0 TD 0 Tc (E)Tj /F7 1 Tf -7.64 0 TD 2.978 Tc [(\016b)866(\016)]TJ /F2 1 Tf -7.21 -2.96 TD 0 Tc ( )Tj ET 90.09 136.65 143.88 -0.48 re f BT 6.48 0 0 6.48 90.09 125.01 Tm (7)Tj 9.96 0 0 9.96 93.33 120.45 Tm -0.001 Tc 0.365 Tw [( T)-17(h)5(at is, in the a)-15(uxi)-12(liar)-17(y)17( )-13(ga)-15(m)18(e)-3( w)10(e)-15( i)-12(g)-7(no)-7(re the p)-7(o)-7(ssib)-7(ilit)-12(y t)-12(h)5(at the p)-7(l)0(a)-15(y)5(ers )-13(m)6(i)0(g)-7(h)5(t )-13(m)6(a)-15(ke d)-7(i)0(ff)7(erent)]TJ -0.3253 -1.1566 TD -0.005 Tc [(a)-7(nno)-23(unc)-7(e)-19(m)2(e)-19(n)1(ts.)]TJ 6.48 0 0 6.48 90.09 102.09 Tm 0 Tc 0 Tw (8)Tj 9.96 0 0 9.96 93.33 97.53 Tm 0.003 Tw [( T)-16(h)6(is f)8(o)-6(llo)-18(w)11(s)3( f)8(r)-4(o)-18(m)7( the )-12(f)8(acts t)-11(h)6(at a)-14(n)-6(y)18( co)-18(m)19(p)-6(ac)-14(t co)-6(nve)-14(x s)-9(u)6(b)-6(s)3(et o)-18(f)8( the i)-11(n)6(terio)-6(r)-4( o)-6(f)8( the p)-6(o)-6(s)3(iti)-11(ve )-24(f)8(easib)-6(le )-12(regio)-18(n)6( )-12(is)]TJ -0.3253 -1.1566 TD 0.232 Tw [(self-generati)-11(n)-6(g f)8(o)-6(r all s)-9(u)-6(f)8(f)-4(icient)-11(l)-11(y)18( )-12(lar)-16(g)6(e )]TJ /F8 1 Tf 10.036 0 0 10.036 263.01 86.01 Tm 0 Tw (E)Tj /F2 1 Tf 9.96 0 0 9.96 270.45 86.01 Tm -0.001 Tc 0.245 Tw [( and)-7( that the se)-15(lf-)7(g)-7(eneratio)-19(n can b)-7(e)-3( co)-7(ns)-10(tructed)-7( to)-7( satis)-10(f)7(i)-12(y)]TJ -18.1084 -1.1566 TD 0.004 Tw [(co)-7(nd)-7(itio)-7(ns a\) thro)-19(ug)-7(h e\) .)]TJ ET endstream endobj 115 0 obj << /ProcSet [/PDF /Text ] /Font << /F1 24 0 R /F2 25 0 R /F4 31 0 R /F5 34 0 R /F6 35 0 R /F7 36 0 R /F8 37 0 R /F10 52 0 R /F11 69 0 R /F12 116 0 R /T66 117 0 R /T67 118 0 R /T68 119 0 R /T69 120 0 R /T70 121 0 R /T71 122 0 R /T72 123 0 R /T73 124 0 R /T74 125 0 R /T75 126 0 R /T76 127 0 R >> /ExtGState << /GS1 26 0 R >> >> endobj 129 0 obj << /Length 10425 >> stream BT /F2 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g /GS1 gs 0 Tc 0 Tw (7)Tj -14.75 -3 TD -0.004 Tc (c\))Tj /F12 1 Tf 0.77 0 TD 0 Tc ( )Tj /F2 1 Tf 0.73 0 TD -0.002 Tc 0.012 Tw [( )10(at)-4( )10(ever)-19(y)18( )10(hi)-4(st)-4(or)-19(y)18( t)-4(h)-2(e p)-12(r)1(ofi)-4(l)-4(e)2(s ei)-4(t)-4(h)-2(er p)-12(r)1(esc)-8(r)1(i)-4(b)-2(e pur)-9(e st)-4(rat)-4(e)-8(g)8(i)-4(es o)-12(r)1( t)-4(h)-2(e st)-4(rat)-4(e)-8(g)8(i)-4(es o)-12(f)]TJ 0 -1.66 TD 0 Tc 0 Tw [(a)4( sta)4(tic)4( Na)4(sh e)4(quilibrium with pa)-16(y)20(o)0(ff 0.)]TJ -1.5 -1.67 TD (d\))Tj /F12 1 Tf 0.83 0 TD ( )Tj /F2 1 Tf 0.67 0 TD 0.001 Tc 0.019 Tw [(if )10(the)5( )10(stra)5(teg)11(i)-1(e)5(s)0( )10(pre)5(s)0(c)5(r)4(ibe)5( )10(pl)-11(a)-15(y)31(in)-9(g)11( th)-9(e)5( sta)5(tic)5( e)5(quilibrium g)11(i)-1(ve)5(n histor)-16(y)21( )]TJ /F5 1 Tf 11.97 0 0 11.97 486.69 664.05 Tm 0.313 Tc (\010\011)Tj /F6 1 Tf -0.5314 0 TD 0.331 Tc (HT)Tj /F2 1 Tf 12 0 0 12 501.21 664.05 Tm 0.001 Tc (, the)Tj -29.76 -1.67 TD 0 Tc 0 Tw [(continuation pa)-6(y)20(o)-10(ffs )]TJ /F5 1 Tf 11.97 0 0 11.97 255.45 644.01 Tm 0.463 Tc (\010\011)Tj /F6 1 Tf -0.6918 0 TD 0.353 Tc [(WY)-1444(W)]TJ /F7 1 Tf 2.2257 0 TD 0 Tc (\036)Tj /F2 1 Tf 12 0 0 12 298.05 644.01 Tm -0.001 Tc 0.001 Tw ( are constant.)Tj -14.33 -1.66 TD 0.001 Tc 0.229 Tw [(e)5(\))4( )10( )10(whe)5(n)-9(e)5(v)1(e)5(r)4( )10(th)-9(e)5( c)5(u)1(rre)5(n)1(t profile)5( is other tha)5(n)1( a)5( sta)5(tic)5( N)-7(a)5(sh e)5(quilibrium, a)5(n)-19(y)]TJ 0 -1.67 TD 0.169 Tw [(de)5(via)5(tion )10(from the)5( c)5(u)1(rre)5(n)1(t period e)5(quilibrium a)5(c)5(tion c)5(o)1(sts a)5(t)-1( le)5(a)5(s)0(t )]TJ ET 0 G 2 J 0 j 0.588 w 10 M []0 d 1 i 489.21 614.25 m 495.21 614.25 l S BT /F5 1 Tf 12 0 0 12 464.49 604.05 Tm -0.069 Tc [(\010\021)-1829(\011)]TJ /F8 1 Tf 1.97 0 TD 0.501 Tc (EI)Tj /F7 1 Tf -0.98 0 TD 0 Tc 0 Tw (\016)Tj /F2 1 Tf 2.61 0 TD 0.002 Tc 0.168 Tw [( in)]TJ -31.8 -1.67 TD -0.002 Tc 0.002 Tw [(current)-4( p)-12(e)2(ri)-4(od ave)-8(r)1(a)-8(g)-2(e pres)-13(ent)-4( val)-4(u)-2(e.)]TJ -3 -1.66 TD -0.004 Tc 0.064 Tw [(Fo)-4(r an)-24(y)16( )]TJ ET 134.01 574.29 m 140.01 574.29 l S BT /F8 1 Tf 12 0 0 12 132.93 564.09 Tm 0 Tc 0 Tw (E)Tj /F2 1 Tf 0.8 0 TD 0.07 Tw [( )10(and )10(an )-10(equilibrium satisf)-7(y)20(in)-10(g)10( the conditions above; w)-8(e)4( refer to the strateg)10(i)-2(es)]TJ -4.37 -1.67 TD 0.01 Tw [(in )10(this equilibrium as the base strateg)-10(y)20(. Our method o)-10(f)3( proof will be to use base strateg)10(i)-12(es)]TJ T* 0.001 Tc -0.001 Tw [(to c)5(onstruc)5(t e)5(quilibrium stra)5(teg)11(i)-1(e)5(s)0( in the)5( )-10(g)11(a)5(me)5( o)-9(f)4( inte)5(re)5(st.)]TJ 3 -1.66 TD -0.005 Tc 0.045 Tw [(Fi)-7(x)-15( a )]TJ /F8 1 Tf 11.963 0 0 11.963 155.85 504.09 Tm 0 Tc 0 Tw (E)Tj /F2 1 Tf 12 0 0 12 163.41 504.09 Tm 0.001 Tc 0.049 Tw [(. )10( )10(Re)5(c)5(a)5(ll )10(from )10(the)5( definition of public)5( informa)5(tion tha)5(t)-1( )]TJ /F8 1 Tf 11.952 0 0 11.952 433.29 504.09 Tm 0 Tc 0 Tw (O)Tj /F2 1 Tf 12 0 0 12 441.81 504.09 Tm 0.001 Tc 0.049 Tw [( is the)5( minimum)]TJ -29.31 -1.67 TD -0.001 Tc 0.001 Tw [(proba)3(bilit)-13(y)19( \(fo)-11(r a)3(n)-21(y)19( )]TJ /F6 1 Tf 11.952 0 0 11.952 188.13 484.05 Tm 0 Tc 0 Tw (N)Tj /F2 1 Tf 12 0 0 12 198.09 484.05 Tm -0.001 Tc 0.001 Tw [(\) of disa)-7(g)9(r)-8(eement )-10(g)9(i)-3(ven that one pl)-13(a)-17(y)19(er lies. D)-9(e)3(fine)]TJ ET q 325.41 465.33 21.6 -12.6 re W* n 331.65 459.09 m 344.37 459.09 l S Q BT /F5 1 Tf 12.016 0 0 12.016 265.53 456.09 Tm 0.44 Tc [(\010\011)-899(\010)509(\021)-1177(\011)]TJ 6.1216 -0.6491 TD 0 Tc 0 Tw (e)Tj /F6 1 Tf -0.5492 1.2782 TD (+)Tj -6.0517 -0.6291 TD (Q)Tj 6.5011 -0.6791 TD (V)Tj /F8 1 Tf -5.6622 0.6791 TD 3.715 Tc (EE)Tj 5.1529 -0.6791 TD 0 Tc (O)Tj /F7 1 Tf -4.0145 0.6791 TD 1.267 Tc (\036\016)Tj /F2 1 Tf 12 0 0 12 347.01 456.09 Tm 0 Tc ( ,)Tj -21.41 -2.75 TD [(whic)4(h is a)4( )-10(proba)4(bilit)-12(y)20( )-20(for )]TJ /F8 1 Tf 11.963 0 0 11.963 216.21 423.09 Tm (E)Tj /F2 1 Tf 12 0 0 12 223.77 423.09 Tm 0.001 Tc 0.009 Tw [( suffic)5(i)-1(e)5(n)1(tl)-11(y)21( l)-11(a)5(rg)11(e)5(,)1( )-10(a)5(nd re)5(ca)5(llin)-9(g)11( tha)5(t)-1( )]TJ ET 404.25 430.29 m 410.25 430.29 l S BT /T77 1 Tf 8.355 0 0 8.355 410.49 427.77 Tm -0.007 Tc (MN)Tj -0.158 -0.8473 TD 0 Tc 0 Tw (A)Tj /F8 1 Tf 11.97 0 0 11.97 403.05 423.09 Tm (Q)Tj /F2 1 Tf 12 0 0 12 424.41 423.09 Tm 0.001 Tc 0.009 Tw [( is the)5( proba)5(bilit)-11(y)31( o)-9(f)]TJ -27.86 -1.67 TD -0.001 Tc 0.001 Tw [(agreem)-13(ent. W)-7(e)3( now define)]TJ ET 274.77 388.89 m 280.77 388.89 l S q 327.93 393.09 18.6 -10.56 re W* n 334.17 388.89 m 340.17 388.89 l S Q 341.37 367.65 m 347.37 367.65 l S BT /F5 1 Tf 12.012 0 0 12.012 211.05 381.69 Tm 0 Tc [(\010)-430(\011)-1409(MIN)-458([)-2927(\010)69(\021)-2877(\011\010)69(\021)-1568(\010)-440(\011\011])]TJ 2.5574 -1.7682 TD 1.578 Tc [(\021\010)1148(\011)1477(M)1581(A)1580(X)1120([)1579(\010)1657(\021)-1309(\011)1577(])]TJ /T78 1 Tf 8.386 0 0 8.386 205.05 386.49 Tm 8.492 Tc [(NM)8502(N)2790(M)8502(N)]TJ 6.811 -0.8585 TD 1.567 Tc [(AA)-4994(A)]TJ 10.1879 -1.6741 TD -0.01 Tc (MN)Tj -5.1226 -0.8585 TD 4.429 Tc (AA)Tj /F6 1 Tf 12.012 0 0 12.012 195.21 381.69 Tm 14.705 Tc (1Q)Tj 5.4644 -1.7682 TD 0 Tc 0 Tw (Q)Tj /F8 1 Tf -3.7861 1.7682 TD 4.396 Tc [(EQ)23(Q)123(E)]TJ 4.6353 -1.7682 TD 5.295 Tc (EQ)Tj /F7 1 Tf -3.4964 1.7682 TD 4.914 Tc [(\036\014)3738(\016)1610(\016)]TJ 0 -1.7682 TD 0.948 Tc [(\036\016)-4783(\016)]TJ /F2 1 Tf 12 0 0 12 414.09 371.01 Tm 0 Tc (,)Tj -27 -3.16 TD 0.001 Tc -0.001 Tw [(whic)5(h is a)5(l)-1(so a)5( proba)5(bility)21( )-10(i)-11(f)4( )]TJ /F5 1 Tf 11.97 0 0 11.97 236.61 333.09 Tm 0.443 Tc (\010\011)Tj /F6 1 Tf -0.4812 0 TD 0 Tc 0 Tw (Q)Tj /F8 1 Tf 0.8421 0 TD (E)Tj /F2 1 Tf 12 0 0 12 252.09 333.09 Tm 0.001 Tc -0.001 Tw ( is.)Tj -10.5 -1.67 TD -0.001 Tc 0.001 Tw [(W)-7(e)3( now consider the public inform)-13(ation game with discount facto)-11(r)]TJ ET 275.61 300.21 m 281.61 300.21 l S BT /F5 1 Tf 12 0 0 12 313.89 290.01 Tm 0.431 Tc (\010\011)Tj /T79 1 Tf 8.379 0 0 8.379 307.89 294.69 Tm 0 Tc 0 Tw (N)Tj /F6 1 Tf 12 0 0 12 298.05 290.01 Tm (1)Tj /F8 1 Tf -1.96 0 TD 3.191 Tc [(EE)2850(E)]TJ /F7 1 Tf 0.96 0 TD 0 Tc (\036)Tj /F2 1 Tf 4.17 0 TD (.)Tj -20.5 -2.25 TD -0.001 Tc 0.091 Tw [(W)-7(e)3( construct a map )]TJ /F8 1 Tf 11.963 0 0 11.963 194.73 263.01 Tm 0 Tc 0 Tw (D)Tj /F2 1 Tf 12 0 0 12 204.09 263.01 Tm 0.09 Tw [( from public histories )]TJ /F5 1 Tf 11.97 0 0 11.97 328.17 263.01 Tm 0.313 Tc (\010\011)Tj ET q 322.29 273.93 16.8 -10.44 re W* n BT /T80 1 Tf 8.355 0 0 8.355 322.29 267.69 Tm 0 Tc 0 Tw (N)Tj ET Q q 315.45 273.93 26.88 -15.96 re W* n BT /F6 1 Tf 11.97 0 0 11.97 315.45 263.01 Tm 0.862 Tc (HT)Tj ET Q BT /F2 1 Tf 12 0 0 12 342.33 263.01 Tm 0.001 Tc 0.089 Tw [( in the)5( g)11(a)5(m)-11(e)5( of inte)5(re)5(st )-10(to )-10(the)5( )-10(se)5(t )-10(of)]TJ -21.02 -1.66 TD 0.149 Tw [(historie)5(s )10(of )10(the)5( sa)5(me)5( le)5(n)-9(g)11(th in the)5( public)5(-inform)-11(a)5(tion ga)5(me)5( )]TJ /F7 1 Tf 11.963 0 0 11.963 395.37 243.09 Tm 0 Tc 0 Tw (\()Tj /F2 1 Tf 12 0 0 12 404.73 243.09 Tm -0.001 Tc 0.151 Tw [(and the s)-12(y)19(mbol )]TJ /F6 1 Tf 11.963 0 0 11.963 487.65 243.09 Tm 0 Tc 0 Tw (0)Tj /F2 1 Tf 12 0 0 12 499.41 243.09 Tm -0.002 Tc 0.152 Tw [( \(for)]TJ -34.11 -1.67 TD 0 Tc 0.12 Tw [(punishment\). This map induces strate)-6(g)10(i)-2(es in the original )-20(game )-10(b)-20(y)20( )-10(assi)-12(g)10(n)0(in)-10(g)10( )-10(the )-10(profile)]TJ T* 0.001 Tc 0.209 Tw [(from )10(the)5( ba)5(se)5( )-10(ga)5(me)5( stra)5(teg)-9(y)21( )-10(whe)5(n)1( the)5( histor)-16(y)21( is ma)5(ppe)5(d to )-10(a)5( history)21( in )]TJ /F7 1 Tf 11.963 0 0 11.963 469.53 203.01 Tm 0 Tc 0 Tw (\()Tj /F2 1 Tf 12 0 0 12 478.89 203.01 Tm -0.001 Tc 0.211 Tw [(, and b)-11(y)]TJ -32.4 -1.66 TD 0.001 Tc 0.019 Tw [(a)5(ssig)11(n)1(in)-9(g)11( )10(the)5( )10(sta)5(tic)5( N)-7(a)5(sh e)5(quilibrium whe)5(n)1( the)5( histor)-16(y)21( is ma)5(ppe)5(d to P. We)5( will show tha)5(t)]TJ 0 -1.67 TD 0 Tc 0 Tw [(the)4(s)-1(e)4( stra)4(teg)10(i)-2(e)4(s)-1( fo)-10(rm a)4(n)0( e)4(quilibrium in the)4( ori)-12(g)10(ina)4(l)-2( )-10(g)10(a)4(me)4(.)]TJ 3 -1.67 TD 0.001 Tc 0.049 Tw [(F)7(o)1(rma)5(l)-1(l)-21(y)21(, we)5( d)-9(e)5(fine)5( the)5( stra)5(teg)11(i)-1(e)5(s)0( in the)5( )-10(g)11(a)5(m)-11(e)5( )]TJ /F6 1 Tf 11.952 0 0 11.952 356.97 143.01 Tm 0 Tc 0 Tw (N)Tj /F2 1 Tf 12 0 0 12 366.93 143.01 Tm -0.001 Tc 0.051 Tw [( b)-11(y)19( the a)-7(c)3(tion taken b)-21(y)19( )-10(the )-10(base)]TJ -23.07 -1.66 TD 0.001 Tc 0.049 Tw [(stra)5(teg)-9(y)21(, )10(or )10(the)5( sta)5(tic)5( N)-7(a)5(sh stra)5(teg)11(i)-1(e)5(s)0( )-10(re)5(spec)5(tive)5(l)-11(y)21(.)1( T)-8(h)1(e)5( ma)5(p )]TJ /F8 1 Tf 11.963 0 0 11.963 385.17 123.09 Tm 0 Tc 0 Tw (D)Tj /F2 1 Tf 12 0 0 12 394.53 123.09 Tm 0.05 Tw [( is defined as follows. W)-6(e)]TJ -25.37 -1.67 TD 0.001 Tc -0.001 Tw [(ma)5(p the)5( initia)5(l null history)21( to the)5( null history)21(.)1( )-10(Give)5(n tha)5(t)-1( a)5(ll historie)5(s of le)5(n)-9(g)11(th )]TJ /F5 1 Tf 11.963 0 0 11.963 489.21 103.05 Tm 0 Tc 0 Tw (\021)Tj /F6 1 Tf -1.5849 0 TD (T)Tj /F7 1 Tf 0.642 0 TD (\016)Tj /F2 1 Tf 12 0 0 12 496.41 103.05 Tm -0.001 Tc 0.011 Tw [( have)]TJ -33.86 -1.67 TD 0.181 Tw [(been mapped, )-10(we de)-7(fine the )-10(map )-20(for )-10(len)-11(g)9(th )]TJ /F6 1 Tf 19.13 0 TD 0 Tc 0 Tw (T)Tj /F2 1 Tf 0.6 0 TD 0.19 Tw [( histories )]TJ /T81 1 Tf 8.355 0 0 8.355 490.05 80.61 Tm 0 Tw (\021)Tj /F5 1 Tf 11.97 0 0 11.97 391.53 83.01 Tm 0.333 Tc [(\010\011)-1022(\010)-641(\010)-1213(\021)392(\011)341(\014)-1382(\014)-981(\011)]TJ /T82 1 Tf 8.355 0 0 8.355 385.89 87.69 Tm 4.921 Tc [(NN)-416(N)2370(N)]TJ 11.3028 -0.8473 TD 2.783 Tc (TT)Tj /F6 1 Tf 11.97 0 0 11.97 379.05 83.01 Tm 0.852 Tc [(HT)-1294(H)10(T)-1615(Y)-644(W)]TJ /T83 1 Tf 8.355 0 0 8.355 483.93 80.61 Tm 0 Tc (\016)Tj ET q 408.33 93.93 64.8 -15.96 re W* n BT /F7 1 Tf 11.97 0 0 11.97 408.33 83.01 Tm 2.619 Tc (\036\016)Tj ET Q BT /F2 1 Tf 12 0 0 12 519.09 83.01 Tm (.)Tj ET endstream endobj 130 0 obj << /ProcSet [/PDF /Text ] /Font << /F2 25 0 R /F5 34 0 R /F6 35 0 R /F7 36 0 R /F8 37 0 R /F12 116 0 R /T77 131 0 R /T78 132 0 R /T79 133 0 R /T80 134 0 R /T81 135 0 R /T82 136 0 R /T83 137 0 R >> /ExtGState << /GS1 26 0 R >> >> endobj 139 0 obj << /Length 18128 >> stream BT /F2 1 Tf 12 0 0 12 303.09 740.01 Tm 0 g /GS1 gs 0 Tc 0 Tw (8)Tj -17.75 -3 TD 0.15 Tw [(When the histor)-7(y)20( is understood, w)-8(e)4( )-10(will )-10(abuse )-10(notation )-10(and )-10(write )]TJ /T84 1 Tf 8.324 0 0 8.324 432.57 700.29 Tm 0 Tw (T)Tj /F6 1 Tf 11.931 0 0 11.931 426.57 704.01 Tm (A)Tj /F2 1 Tf 12 0 0 12 437.85 704.01 Tm 0.001 Tc 0.159 Tw [( to be)5( the)5( a)5(c)5(tion)]TJ -28.98 -1.66 TD 0 Tc 0 Tw [(taken in the base str)-7(a)4(te)-6(g)-10(y)20( )-10(g)10(i)-2(ven the histor)-17(y)20( )]TJ /F5 1 Tf 11.97 0 0 11.97 306.57 684.09 Tm 1.015 Tc [(\010\010)-491(\021)1094(\011)1013(\011)]TJ /T85 1 Tf 8.355 0 0 8.355 317.37 688.77 Tm 0 Tc (N)Tj /F6 1 Tf 11.97 0 0 11.97 310.53 684.09 Tm 0.873 Tc (HT)Tj /F8 1 Tf -0.9023 0 TD 0 Tc (D)Tj ET q 1 i 334.77 695.01 24 -15.96 re W* n BT /F7 1 Tf 11.97 0 0 11.97 334.77 684.09 Tm (\016)Tj ET Q BT /F2 1 Tf 12 0 0 12 362.01 684.09 Tm [(. )-10(I)23(t)-2( is conv)-10(enient also to define)]TJ ET q 1 i 323.01 673.89 18.6 -10.56 re W* n 0 G 2 J 0 j 0.588 w 10 M []0 d 329.25 669.69 m 335.25 669.69 l S Q 0 G 2 J 0 j 0.588 w 10 M []0 d 1 i 322.05 653.97 m 328.05 653.97 l 261.81 657.93 m 400.77 657.93 l S BT /F5 1 Tf 11.97 0 0 11.97 276.21 662.49 Tm 0.002 Tc [(\010)-441(\011)-1113(\010)80(\021)-2897(\011\010)70(\021)-1573(\010)-441(\011\011)]TJ -4.712 -0.6316 TD 0.423 Tc [(\010\014)-159(\011)]TJ /T85 1 Tf 8.355 0 0 8.355 270.33 667.29 Tm 7.233 Tc [(NM)7240(N)]TJ 7.6405 -0.8617 TD 0 Tc (A)Tj -14.4049 -0.0431 TD (N)Tj 13.7155 -0.9766 TD -0.022 Tc (MN)Tj ET q 326.97 653.97 16.8 -12 re W* n BT 8.355 0 0 8.355 326.97 644.37 Tm 0 Tc (A)Tj ET Q BT /F6 1 Tf 11.97 0 0 11.97 260.49 662.49 Tm 8.896 Tc (1Q)Tj -4.4413 -0.6316 TD 0.822 Tc (PA)Tj /F8 1 Tf 6.1155 0.6316 TD 3.521 Tc [(EQ)-769(E)]TJ -3.8698 -0.6316 TD 0 Tc (E)Tj ET q 320.85 661.17 24 -19.2 re W* n BT 11.97 0 0 11.97 320.85 646.77 Tm (Q)Tj ET Q BT /F7 1 Tf 11.97 0 0 11.97 292.89 662.49 Tm 1.153 Tc [(\016\016)-2165(\016)]TJ -3.7596 -0.6316 TD 0 Tc (\036)Tj /F2 1 Tf 12 0 0 12 403.53 654.93 Tm (.)Tj -26.12 -2.9 TD -0.002 Tc 0.452 Tw [(Not)-4(i)-4(ce t)-4(h)-2(at)-4( we h)-12(a)2(ve chose)-8(n)-2( )]TJ /F5 1 Tf 11.97 0 0 11.97 258.57 620.13 Tm 0.443 Tc [(\010\011)441(\014)-881(\010)0(\011)]TJ /T86 1 Tf 8.355 0 0 8.355 286.53 624.81 Tm 0 Tc 0 Tw (N)Tj /F6 1 Tf 11.97 0 0 11.97 252.81 620.13 Tm 1.526 Tc (Q1)Tj /F8 1 Tf 0.8421 0 TD 2.378 Tc (EE)Tj /F2 1 Tf 12 0 0 12 308.13 620.13 Tm 0 Tc 0.46 Tw [( so that )]TJ /F5 1 Tf 11.97 0 0 11.97 376.65 620.13 Tm 0.423 Tc [(\010\014)-159(\011)-882(\021)]TJ /T87 1 Tf 8.355 0 0 8.355 370.65 624.81 Tm 0 Tc 0 Tw (N)Tj ET q 364.17 631.05 40.08 -15.96 re W* n BT /F6 1 Tf 11.97 0 0 11.97 364.17 620.13 Tm 0.822 Tc (PA)Tj ET Q BT /F8 1 Tf 11.97 0 0 11.97 391.05 620.13 Tm (E)Tj /F7 1 Tf 1.1329 0 TD (b)Tj /F2 1 Tf 12 0 0 12 424.41 620.13 Tm -0.003 Tc 0.463 Tw [(. Noti)-5(ce al)-5(so t)-5(h)-3(at)]TJ ET 165.81 607.29 m 171.81 607.29 l S BT /F5 1 Tf 11.97 0 0 11.97 106.05 600.09 Tm 0 Tc [(\010)-433(\011)-1365(MIN)]TJ /T87 1 Tf 8.355 0 0 8.355 100.05 604.77 Tm 8.871 Tc (NN)Tj /F6 1 Tf 11.97 0 0 11.97 90.21 600.09 Tm 0 Tc 0 Tw (1)Tj /F8 1 Tf 1.6843 0 TD 4.083 Tc (EQ)Tj /F7 1 Tf 1.1229 0 TD 0 Tc (p)Tj /F2 1 Tf 12 0 0 12 186.09 600.09 Tm (, so if )Tj ET 246.57 607.29 m 252.57 607.29 l S BT /F5 1 Tf 11.97 0 0 11.97 217.77 600.09 Tm -0.01 Tc [(MI)-10(N)-3760(\021)-71(\017)-121(\022)]TJ /T88 1 Tf 8.355 0 0 8.355 252.93 604.77 Tm -0.022 Tc (MN)Tj -1.8527 -0.8474 TD 1.159 Tc (AA)Tj /F8 1 Tf 11.97 0 0 11.97 245.37 600.09 Tm 0 Tc (Q)Tj /F7 1 Tf 2.0452 0 TD (\037)Tj /F2 1 Tf 12 0 0 12 304.05 600.09 Tm -0.001 Tc 0.001 Tw [(, we also hav)-11(e)3( )]TJ /F5 1 Tf 11.97 0 0 11.97 389.37 600.09 Tm 0.423 Tc [(\010\014)-159(\011)-942(\020)]TJ /T88 1 Tf 8.355 0 0 8.355 383.37 604.77 Tm 0 Tc 0 Tw (N)Tj /F6 1 Tf 11.97 0 0 11.97 376.89 600.09 Tm 0.822 Tc (PA)Tj /F8 1 Tf 2.2457 0 TD 0 Tc (E)Tj /F7 1 Tf 1.1229 0 TD (p)Tj /F2 1 Tf 12 0 0 12 438.09 600.09 Tm (.)Tj /F10 1 Tf -29 -3.33 TD -0.001 Tc 0.131 Tw [(Case 0:)]TJ /F2 1 Tf 3.26 0 TD 0 Tc 0.14 Tw [( I)13(f)3( )10(th)-10(e )10(cur)-7(r)3(ent )10(base )10(strateg)-10(y)20( pro)-10(f)3(ile is a static Nash )-10(equilibrium use the public)]TJ -3.26 -1.67 TD [(randomiz)-6(ation )]TJ /T89 1 Tf 8.391 0 0 8.391 172.29 544.89 Tm 0 Tw (N)Tj -0.1001 -1.0154 TD (T)Tj /F6 1 Tf 12.028 0 0 12.028 163.53 540.09 Tm (W)Tj /F2 1 Tf 12 0 0 12 179.49 540.09 Tm -0.001 Tc 0.001 Tw [( choosing)9( e)-7(ach )]TJ 6.938 0 0 6.938 262.65 545.37 Tm 2.873 Tc (**)Tj /F4 1 Tf 12 0 0 12 256.77 540.09 Tm 1.286 Tc (yY)Tj /F11 1 Tf 0.96 0 TD 0 Tc 0 Tw (\316)Tj /F2 1 Tf 1.96 0 TD [( with proba)4(bilit)-12(y)30( )]TJ ET q 390.69 551.13 76.08 -17.16 re W* n BT /F5 1 Tf 12 0 0 12 390.69 540.09 Tm 0.441 Tc [(\010\011)-760(\010)-30(\012)170(\\)-558(\012)440(\011)]TJ ET Q BT /T90 1 Tf 6 0 0 6 415.05 535.17 Tm (T)Tj /T91 1 Tf 8.379 0 0 8.379 384.69 544.89 Tm 2.671 Tc (NM)Tj 3.1221 -0.845 TD 0 Tc (A)Tj ET q 374.85 551.13 91.92 -17.16 re W* n BT /F6 1 Tf 12 0 0 12 374.85 540.09 Tm 3.301 Tc [(1Y)2100(9)]TJ ET Q BT /F8 1 Tf 12 0 0 12 395.01 540.09 Tm 0.361 Tc (EQ)Tj /F2 1 Tf 5.98 0 TD 0.001 Tc -0.001 Tw [( a)5(nd )-10(se)5(tting)]TJ /T92 1 Tf 8.355 0 0 8.355 167.73 517.65 Tm 0 Tc 0 Tw (\021)Tj /F5 1 Tf 11.97 0 0 11.97 98.61 520.05 Tm -0.059 Tc [(\010)-1043(\010)-1595(\021\011)-61(\014)-1764(\014)-1373(\011)-1414(\010)-632(\010)-1033(\010)-1605(\021\011)-51(\011)-61(\014)-661(\012)-61(\011)]TJ /T93 1 Tf 8.355 0 0 8.355 109.29 524.73 Tm 5.337 Tc [(NN)2771(N)14(N)]TJ 5.8165 -0.8474 TD 2.798 Tc (TT)Tj /F6 1 Tf 11.97 0 0 11.97 102.57 520.05 Tm 0.852 Tc [(HT)-1605(Y)-654(W)-2759(H)10(T)-1996(Y)]TJ /F8 1 Tf -0.9123 0 TD 9.784 Tc (DD)Tj /T94 1 Tf 8.355 0 0 8.355 161.49 517.65 Tm 0 Tc (\016)Tj /F7 1 Tf 11.97 0 0 11.97 126.57 520.05 Tm 5.273 Tc [(\016\036)1692(\016)]TJ /F2 1 Tf 12 0 0 12 300.09 520.05 Tm 0.001 Tc 0.869 Tw [( a)5(nd with the)5( )-10(re)5(ma)5(inin)-9(g)11( )-10(prob)-9(a)5(b)1(ilit)-11(y)]TJ /T95 1 Tf 8.355 0 0 8.355 167.61 497.73 Tm 0 Tc 0 Tw (\021)Tj /F5 1 Tf 11.97 0 0 11.97 98.61 500.13 Tm 0.984 Tc [(\010\010)-552(\021)1043(\011)982(\014)-721(\014)-330(\011)]TJ /T96 1 Tf 8.355 0 0 8.355 109.29 504.81 Tm 5.337 Tc [(NN)2786(N)]TJ 5.8165 -0.8473 TD 2.783 Tc (TT)Tj /F6 1 Tf 11.97 0 0 11.97 102.57 500.13 Tm 0.852 Tc [(HT)-1605(Y)-644(W)-1506(0)]TJ /F8 1 Tf -0.9123 0 TD 0 Tc (D)Tj /T97 1 Tf 8.355 0 0 8.355 161.49 497.73 Tm (\016)Tj /F7 1 Tf 11.97 0 0 11.97 126.57 500.13 Tm 5.273 Tc (\016\036)Tj /F2 1 Tf 12 0 0 12 223.05 500.13 Tm 0 Tc (.)Tj /F10 1 Tf -11.08 -3.34 TD -0.001 Tc 0.001 Tw (Case 1:)Tj /F2 1 Tf 3.13 0 TD -0.013 Tc 0.023 Tw [( If)-10( )]TJ /F7 1 Tf 11.963 0 0 11.97 151.89 460.05 Tm 3.885 Tc (\011\012)Tj /F5 1 Tf 11.97 0 0 11.97 170.13 460.05 Tm 1.506 Tc [(\010\021)1585(\011)]TJ /T98 1 Tf 8.355 0 0 8.355 164.13 464.73 Tm 0 Tc 0 Tw (N)Tj /F6 1 Tf 11.97 0 0 11.97 157.29 460.05 Tm 0.873 Tc [(HT)-2998(0)]TJ /F8 1 Tf -1.163 0 TD 0 Tc (D)Tj /F7 1 Tf 3.1881 0 TD 1.684 Tc (\016\036)Tj /F2 1 Tf 12 0 0 12 235.65 460.05 Tm 0 Tc (, )Tj /F7 1 Tf 11.968 0 0 11.97 251.85 460.05 Tm 2.269 Tc (\011\012)Tj /F5 1 Tf 11.97 0 0 11.97 270.09 460.05 Tm 0.313 Tc (\010\011)Tj /T99 1 Tf 8.355 0 0 8.355 264.21 464.73 Tm 0 Tc (N)Tj /F6 1 Tf 11.97 0 0 11.97 257.25 460.05 Tm 0.873 Tc [(HT)-1394(0)]TJ /F8 1 Tf -1.163 0 TD 0 Tc (D)Tj /F7 1 Tf 4.0403 0 TD (\036)Tj /F2 1 Tf 12 0 0 12 316.65 460.05 Tm [(, so punishment is absorbing)10(.)]TJ /F10 1 Tf -18.88 -3.43 TD -0.001 Tc 0.001 Tw (Case 2: )Tj /F2 1 Tf 3.39 0 TD -0.013 Tc [(If)-10( )]TJ /F7 1 Tf 11.963 0 0 11.97 151.89 418.89 Tm 3.885 Tc (\011\012)Tj /F5 1 Tf 11.97 0 0 11.97 170.13 418.89 Tm 1.506 Tc [(\010\021)1585(\011)]TJ /T99 1 Tf 8.355 0 0 8.355 164.13 423.57 Tm 0 Tc 0 Tw (N)Tj /F6 1 Tf 11.97 0 0 11.97 157.29 418.89 Tm 0.873 Tc [(HT)-2998(0)]TJ /F8 1 Tf -1.163 0 TD 0 Tc (D)Tj /F7 1 Tf 3.1881 0 TD 1.684 Tc (\016v)Tj /F2 1 Tf 12 0 0 12 235.65 418.89 Tm -0.001 Tc 0.001 Tw ( and )Tj /T100 1 Tf 8.379 0 0 8.379 275.49 416.61 Tm -0.078 Tc [(\021\014)-32(\021)-4039(\021)0(\014)-60(\022)]TJ /T101 1 Tf -1.0741 0.845 TD 4.562 Tc (NN)Tj -0.0859 -0.845 TD 4.794 Tc (TT)Tj /F6 1 Tf 12 0 0 12 260.01 418.89 Tm 3.091 Tc (YY)Tj /T102 1 Tf 8.379 0 0 8.379 269.25 416.61 Tm 4.345 Tc (\016\016)Tj /F7 1 Tf 12 0 0 12 290.13 418.89 Tm 0 Tc 0 Tw (\036)Tj /F2 1 Tf 3.33 0 TD [(, use the public randomiz)-6(ation )]TJ /T103 1 Tf 8.391 0 0 8.391 487.89 423.69 Tm (N)Tj -0.1001 -1.0154 TD (T)Tj /F6 1 Tf 12.028 0 0 12.028 479.13 418.89 Tm (W)Tj /F2 1 Tf 12 0 0 12 495.09 418.89 Tm 0.001 Tc -0.001 Tw ( so)Tj -33.75 -1.52 TD [(tha)5(t)-1( with proba)5(bilit)-11(y)21( )]TJ /F5 1 Tf 12.028 0 0 12.028 205.41 400.65 Tm 0.728 Tc [(\010\014)150(\011)]TJ /T104 1 Tf 8.391 0 0 8.391 199.41 405.45 Tm 0 Tc 0 Tw (N)Tj 1.8592 -1.0154 TD (T)Tj /F6 1 Tf 12.028 0 0 12.028 192.93 400.65 Tm 0.816 Tc (PA)Tj /F8 1 Tf 2.544 0 TD 0 Tc (E)Tj /F2 1 Tf 12 0 0 12 235.17 400.65 Tm -0.001 Tc 0.001 Tw ( we have)Tj /T105 1 Tf 8.355 0 0 8.355 167.73 369.21 Tm 14.96 Tc (\021\021)Tj /F5 1 Tf 11.97 0 0 11.97 98.61 371.61 Tm 0.984 Tc [(\010\010)-552(\021)1043(\011)982(\014)-721(\014)-330(\011)-371(\010)411(\010\010)-552(\021)1043(\011)982(\011)992(\014)-781(\011)]TJ /T106 1 Tf 8.355 0 0 8.355 109.29 376.29 Tm 5.337 Tc [(NN)2771(N)14(N)-561(N)]TJ 5.8165 -0.8473 TD 2.798 Tc [(TT)-9220(T)]TJ /F6 1 Tf 11.97 0 0 11.97 102.57 371.61 Tm 0.852 Tc [(HT)-1605(Y)-654(W)-2759(H)10(T)-2006(Y)]TJ /F8 1 Tf -0.9123 0 TD 9.784 Tc (DD)Tj /T107 1 Tf 8.355 0 0 8.355 161.49 369.21 Tm 14.685 Tc (\016\016)Tj /F7 1 Tf 11.97 0 0 11.97 126.57 371.61 Tm 5.273 Tc [(\016\036)1692(\016)]TJ /F2 1 Tf 12 0 0 12 90.09 344.73 Tm -0.001 Tc (and )Tj /T108 1 Tf 8.355 0 0 8.355 187.89 342.33 Tm 0 Tc 0 Tw (\021)Tj /F5 1 Tf 11.97 0 0 11.97 118.89 344.73 Tm 0.984 Tc [(\010\010)-552(\021)1043(\011)982(\014)-721(\014)-330(\011)]TJ /T109 1 Tf 8.355 0 0 8.355 129.57 349.41 Tm 5.337 Tc [(NN)2786(N)]TJ 5.8165 -0.8474 TD 2.783 Tc (TT)Tj /F6 1 Tf 11.97 0 0 11.97 122.85 344.73 Tm 0.852 Tc [(HT)-1605(Y)-644(W)-1506(0)]TJ /F8 1 Tf -0.9123 0 TD 0 Tc (D)Tj /T110 1 Tf 8.355 0 0 8.355 181.77 342.33 Tm (\016)Tj /F7 1 Tf 11.97 0 0 11.97 146.85 344.73 Tm 5.273 Tc (\016\036)Tj /F2 1 Tf 12 0 0 12 243.33 344.73 Tm -0.001 Tc 0.001 Tw ( otherwise.)Tj /F10 1 Tf -12.77 -3.34 TD 0.031 Tw [(Case 3:)]TJ /F2 1 Tf 3.16 0 TD -0.013 Tc 0.053 Tw [( If)-10( )]TJ /F7 1 Tf 11.963 0 0 11.97 152.97 304.65 Tm 3.885 Tc (\011\012)Tj /F5 1 Tf 11.97 0 0 11.97 171.21 304.65 Tm 1.506 Tc [(\010\021)1585(\011)]TJ /T111 1 Tf 8.355 0 0 8.355 165.21 309.33 Tm 0 Tc 0 Tw (N)Tj /F6 1 Tf 11.97 0 0 11.97 158.37 304.65 Tm 0.873 Tc [(HT)-2998(0)]TJ /F8 1 Tf -1.163 0 TD 0 Tc (D)Tj /F7 1 Tf 3.1881 0 TD 1.684 Tc (\016v)Tj /F2 1 Tf 12 0 0 12 236.73 304.65 Tm -0.001 Tc 0.031 Tw [( and )]TJ /T112 1 Tf 8.391 0 0 8.391 271.05 300.69 Tm 3.211 Tc (\021\022)Tj /T113 1 Tf -0.3003 1.044 TD 3.125 Tc (NN)Tj -0.1001 -1.044 TD 3.356 Tc (TT)Tj /F6 1 Tf 12.028 0 0 12.028 262.05 304.65 Tm 2.085 Tc (YY)Tj /F7 1 Tf 1.4965 0 TD 0 Tc 0 Tw (v)Tj /F2 1 Tf 12 0 0 12 308.01 304.65 Tm 0.04 Tw [(, use the public randomiz)-6(ation )]TJ /T114 1 Tf 8.391 0 0 8.391 468.21 309.45 Tm 0 Tw (N)Tj -0.1001 -1.0154 TD (T)Tj /F6 1 Tf 12.028 0 0 12.028 459.45 304.65 Tm (W)Tj /F2 1 Tf 12 0 0 12 475.41 304.65 Tm 0.04 Tw [( choosing)]TJ -32.11 -1.66 TD -0.003 Tc (each )Tj 6.938 0 0 6.938 143.73 290.01 Tm 2.873 Tc (**)Tj /F4 1 Tf 12 0 0 12 137.85 284.73 Tm 1.286 Tc (yY)Tj /F11 1 Tf 0.96 0 TD 0 Tc 0 Tw (\316)Tj /F2 1 Tf 1.96 0 TD 0.001 Tc 1.649 Tw [( with proba)5(bilit)-11(y)21( )]TJ /F7 1 Tf 11.963 0 0 12 316.05 284.73 Tm 3.473 Tc (<>)Tj /F5 1 Tf 12 0 0 12 320.25 284.73 Tm 1.58 Tc [(\021\010)1139(\011)-101(\010)1109(\012)1309(\\)581(\012)1579(\011)]TJ /T115 1 Tf 6 0 0 6 375.33 279.81 Tm 0 Tc 0 Tw (T)Tj /T116 1 Tf 8.379 0 0 8.379 372.09 289.53 Tm (M)Tj -0.1146 -0.845 TD (A)Tj /F6 1 Tf 12 0 0 12 339.33 284.73 Tm 3.261 Tc [(QY)2060(9)]TJ ET q 349.53 295.77 39.6 -17.4 re W* n 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prob)-9(a)5(b)1(ilit)-11(y)]TJ /T117 1 Tf 8.355 0 0 8.355 167.61 242.25 Tm 0 Tc 0 Tw (\021)Tj /F13 1 Tf 11.97 0 0 11.97 98.61 244.65 Tm 0.982 Tc [(\010\010)-552(\021)1042(\011)982(\014)-722(\014)-331(\011)]TJ /T111 1 Tf 8.355 0 0 8.355 109.29 249.33 Tm 5.337 Tc [(NN)2786(N)]TJ /T121 1 Tf 5.8165 -0.8473 TD 2.783 Tc (TT)Tj /F14 1 Tf 11.97 0 0 11.97 102.57 244.65 Tm 0.852 Tc [(HT)-1604(Y)-652(W)-1504(0)]TJ /F15 1 Tf -0.9123 0 TD 0 Tc (D)Tj /T119 1 Tf 8.355 0 0 8.355 161.49 242.25 Tm (\016)Tj /F16 1 Tf 11.97 0 0 11.97 126.57 244.65 Tm 5.273 Tc (\016\036)Tj /F2 1 Tf 12 0 0 12 223.05 244.65 Tm 0 Tc (.)Tj -11.08 -3.33 TD 0.08 Tw [(The)4( re)4(ma)4(ind)-10(e)4(r of the)4( p)-10(r)3(oof, whic)4(h is in the)4( a)4(p)0(p)-10(e)4(ndix)-10(,)0( ve)4(rifie)4(s)-1( tha)4(t)-2( the)4(s)-1(e)4( stra)4(teg)10(i)-12(e)4(s)-1( )-10(form)]TJ 0 -1.67 TD 0.001 Tc -0.001 Tw [(a)5(n)1( e)5(quilibrium in g)11(a)5(me)5( )]TJ /F4 1 Tf 9.54 0 TD 0 Tc (n )Tj /F2 1 Tf 0.75 0 TD -0.002 Tc 0.002 Tw [(wi)-4(t)-4(h)-2( 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