博弈论考试题目答案

14.12GameTheory—MidtermI

10/9/2002

Prof.MuhametYildiz

Instructions.Thisisanopenbookexam;youcanuseanywrittenmaterial.Youhaveonehourand20minutes.Eachquestionis35points.Goodluck!

1.Considerthefollowinggameinextensiveform.

博弈论考试题目答案

1

1,4

(a)Applybackwardsinductioninthisgame.Statetherationality/knowledgeas-

sumptionsnecessaryforeachstepinthisprocess.

Thebackwardsinductionoutcomeisasbelow.We rsteliminateactionr1forplayer2,byassumingthatplayer2issequentiallyrationalandhencewillnotplayr1,whichisconditionallydominatedbyl1.Wealsoeliminateactionrforplayer1,assumingthatplayer1issequentiallyrational.Thisisbecauserisconditionallydominatedbyl.Second,assumingthatplayer2issequentiallyrationalandthatplayer2knowsthatplayer1issequentiallyrational,weeliminater2.Thisisbecause,knowingthatplayer1issequentiallyrational,player2wouldknowthat1willnotplayr,andhencer2wouldleadtopayo of2.Beingsequentiallyrationalshemustplayl2.Finally,assumingthat(i)player1issequentiallyrational,(ii)player1knowsthatplayer2issequentiallyrational,and(iii)player1knowsthatplayer2knowsthatplayer1issequentiallyrational,weeliminateR.Thisisbecause(ii)and(iii)leadplayer1toconcludethat2willplayl1andl2,andthusby(i)heplaysL.

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