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1、GameswithCommunication(I)11.ContractsandCorrelatedStrategies1.1What’sMeaningofGamewithContract?Considerthemostextremekindofimplicitcoordinationassumption:Playerscancommunicatewitheachother,signjointlybindingcontractstocoordinatetheirstrategies.SuchasinTable6.1.Inthisgame,theuniquee
2、quilibriumis(y,1y).Thepayoffis(1,1).2Table6.1:Agameinstrategic-formC2C1x2y2x12,20,6y16,01,12Nowsupposethatsomeoutsideintervenerpresentedthetwoplayerswithacontract:“We,theundersigned,promisetochoosexorxifthis12contractissignedbybothplayers.Ifitissignedbyonlyoneplayer,thenheorshewill
3、choosey1ory.”2Table6.1:Agameinstrategic-formC2C1x2y2x12,20,6y16,01,13Theoptionforeachplayertosignthecontractcanbeintroducedintothegamedescription,asthestrategys,showniinTable6.2.Thistransformedgamehasanequilibriumat(s,s),whichis12theuniqueperfectequilibriumandgivesthepayoffallocati
4、on(2,2).Table6.2:Agameinstrategic-form,includingonecontract-signingstrategyforeachplayerC2C1xys222x2,20,60,61y6,01,11,11s6,01,12,214Table6.2:Agameinstrategic-form,includingonecontract-signingstrategyforeachplayerC2C1xys222x2,20,60,61y6,01,11,11s6,01,12,21Evenbetterexpectedpayoffsco
5、uldbeachievedifthecontractcommittedtheplayerstoacorrelatedorjointlyrandomizedstrategy.Forexample,anothercontractmightspecifythat,ifbothplayerssignthecontract,thenacoinwillbetossedafterwhichoccurstheywillimplement(x,y)ifHeads,and(y,x)ifTails.12125Table6.2:Agameinstrategic-form,inclu
6、dingonecontract-signingstrategyforeachplayerC2C1xys222x2,20,60,61y6,01,11,11s6,01,12,21Theexpectedpayoffallocationwhenbothplayerssignthissecondcontractis(3,3).6Table6.3:Agameinstrategic-form,includingonecontract-signingstrategyforeachplayerC2C1xyssˆ2222x2,20,60,60,61y6,01,11,11,11s
7、6,01,12,21,11sˆ6,01,11,13,31Assumingthattheplayersmustmaketheirsigningdecisionsindependentlyandthateachplayercansignonlyonecontract,andletting^sdenoteplayeri’soptiontosignthesecondtract,ithetransformedgamebecomesasshowninTable6.3.7Table6.3:Agameinstrategic-form,includingonecontract
8、-signingstrategyforeachpla
