國(guó)外博弈論課件lecture(14)-資料下載頁(yè)
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【正文】 e TheoryLecture 19 21 Finitely repeated game ? A finitely repeated game is a dynamic game of plete information in which a (simultaneousmove) game is played a finite number of times, and the previous plays are observed before the next play. ? The finitely repeated game has a unique subgame perfect Nash equilibrium if the stage game (the simultaneousmove game) has a unique Nash equilibrium. The Nash equilibrium of the stage game is played in every stage. June 16, 2021 73347 Game TheoryLecture 19 22 What happens if the stage game has more than one Nash equilibrium? ? Two players play the following simultaneous move game twice ? The oute of the first play is observed before the second play begins ? The payoff for the entire game is simply the sum of the payoffs from the two stages. That is, the discount factor is 1. ? Question: can we find a subgame perfect Nash equilibrium in which M1, M2 are played? Or, can the two players cooperate in a subgame perfect Nash equilibrium? Player 2 L2 M2 R2 Player 1 L1 1 , 1 5 , 0 0 , 0 M1 0 , 5 4 , 4 0 , 0 R1 0 , 0 0 , 0 3 , 3 June 16, 2021 73347 Game TheoryLecture 19 23 Informal game tree 1 L1 R1 2 2 L2 R2 M2 L2 R2 M2 L2 R2 M2 2 L1 R1 2 2 L2 R2 M2 L2 R2 M2 L2 R2 M2 2 M1 (1, 1) (5, 0) (0, 5) (4, 4) (0, 0) M1 (0, 0) (0, 0) (0, 0) (3, 3) 1 (1, 1) (5, 0) (0, 5) (0, 0) (0, 0) (0, 0) (0, 0) (3, 3) (4, 4) 1 1 June 16, 2021 73347 Game TheoryLecture 19 24 Informal game tree and backward induction 1 L1 R1 2 2 L2 R2 M2 L2 R2 M2 L2 R2 M2 2 L1 R1 2 2 L2 R2 M2 L2 R2 M2 L2 R2 M2 2 M1 (1, 1) (5, 0) (0, 5) (4, 4) (0, 0) M1 (0, 0) (0, 0) (0, 0) (3, 3) 1 (1, 1) (5, 0) (0, 5) (0, 0) (0, 0) (0, 0) (0, 0) (3, 3) (4, 4) (1, 1) (1, 1) (1, 1) (3, 3) (1, 1) (1, 1) (1, 1) (1, 1) (1, 1) + 1 1 June 16, 2021 73347 Game TheoryLecture 19 25 Twostage repeated game Player 2 L2 M2 R2 Player 1 L1 2 , 2 6 , 1 1 , 1 M1 1 , 6 7 , 7 1 , 1 R1 1 , 1 1 , 1 4 , 4 ? Subgame perfect Nash equilibrium: ? At stage 1, player 1 plays M1, and player 2 plays M2. ? At stage 2, ? player 1 plays R1 if the first stage oute is ( M1, M2 ), or plays L1 if the first stage oute is not ( M1, M2 ) ? player 2 plays R2 if the first stage oute is ( M1, M2 ), or plays L2 if the first stage oute is not ( M1, M2 ) The payoffs of the 2nd stage has been added to the first stage game. June 16, 2021 73347 Game TheoryLecture 19 26 Summary ? Tariffs and imperfect international petition ( of Gibbons) ? Finitely repeated games ? Next time ? Infinitely repeated games ? Reading lists ? Sec AB of Gibbons
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