國外博弈論課件lecture(20)-資料下載頁
2025-10-10 13:59本頁面
【正文】 play continues to the third period) ? At the beginning of third period, player 1 receives a share s of the dollar, leaving 1s for player 2, where 0s 1. ? The players are impatient. They discount the payoff by a fact ?, where 0 ? 1 June 5, 2021 73347 Game TheoryLecture 13 26 Sequential bargaining ( of Gibbons) Player 2 accept reject propose an offer ( s2 , 1s2 ) Period 1 Player 1 accept propose an offer ( s1 , 1s1 ) s1 , 1s1 Player 1 s2 , 1s2 s , 1s Period 2 Period 3 reject Player 2 June 5, 2021 73347 Game TheoryLecture 13 27 Solve sequential bargaining by backward induction ? Period 2: ? Player 1 accepts s2 if and only if s2 ? ?s. (We assume that each player will accept an offer if indifferent between accepting and rejecting) ? Player 2 faces the following two options: (1) offers s2 = ?s to player 1, leaving 1s2 = 1?s for herself at this period, or (2) offers s2 ?s to player 1 (player 1 will reject it), and receives 1s next period. Its discounted value is ?(1s) ? Since ?(1s)1?s, player 2 should propose an offer (s2* , 1s2* ), where s2* = ?s. Player 1 will accept it. June 5, 2021 73347 Game TheoryLecture 13 28 Sequential bargaining ( of Gibbons) Player 2 accept reject propose an offer ( s2 , 1s2 ) Period 1 Player 1 accept propose an offer ( s1 , 1s1 ) s1 , 1s1 Player 1 s2 , 1s2 s , 1s Period 2 Period 3 reject Player 2 ?s , 1? s June 5, 2021 73347 Game TheoryLecture 13 29 Solve sequential bargaining by backward induction ? Period 1: ? Player 2 accepts 1s1 if and only if 1s1 ? ?(1s2*)= ?(1 ?s) or s1 ? 1?(1s2*), where s2* = ?s. ? Player 1 faces the following two options: (1) offers 1s1 = ?(1s2*)=?(1 ?s) to player 2, leaving s1 = 1?(1s2*)=1?+??s for herself at this period, or (2) offers 1s1 ?(1s2*) to player 2 (player 2 will reject it), and receives s2* = ?s next period. Its discounted value is ??s ? Since ??s 1?+??s, player 1 should propose an offer (s1* , 1s1* ), where s1* = 1?+??s June 5, 2021 73347 Game TheoryLecture 13 30 Summary ? Subgame perfect Nash equilibrium ? Backward induction ? Next time ? Stackelberg Model of duopoly ? Wages and employment in a unionized firm ? Reading lists ? Sec of Gibbons ? Sec of Osborn
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