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国外博弈论课件lecture20
June 17, 2003 73-347 Game Theory--Lecture 20 June 17, 2003 Lecture 20 Dynamic Games of Complete Information Dynamic Games of Complete and Imperfect Information Outline of dynamic games of complete information Dynamic games of complete information Extensive-form representation Dynamic games of complete and perfect information Game tree Subgame-perfect Nash equilibrium Backward induction Applications Dynamic games of complete and imperfect information More applications Repeated games Today’s Agenda Review of previous class Repeated games Infinitely repeated games Two-stage repeated game Two-stage prisoners’ dilemma Two players play the following simultaneous move game twice The outcome 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: what is the subgame perfect Nash equilibrium? Game tree of the two-stage prisoners’ dilemma Informal game tree of the two-stage prisoners’ dilemma Informal game tree of the two-stage prisoners’ dilemma two-stage prisoners’ dilemma The subgame-perfect Nash equilibrium(L1 L1L1L1L1, L2 L2L2L2L2) Player 1 plays L1 at stage 1, and plays L1 at stage 2 for any outcome of stage 1.Player 2 plays L2 at stage 1, and plays L2 at stage 2 for any outcome of stage 1. Finitely repeated game A finitely repeated game is a dynamic game of complete information in which a (simultaneous-move) 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 simultaneous-move game) has a unique Nash equilibrium. The Nash equilibrium of the stage game is played in every stage. What happens if the stage game has more than one Nash equilibrium? Two players play the following simultaneous move game twice The outcome of the first play is observed before the second play begins The payoff for the
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