微觀經(jīng)濟(jì)學(xué)趙耀輝第28章-wenkub
2023-05-26 17:01:23 本頁面
【正文】 only a few firms) ?The study of cartels。 establish reputation –Sequential moves Sequential Game ?When such a game is sequential it is sometimes possible to argue that one of the Nash equilibria is more likely to occur than the other. Who Plays When? ?When players chose their strategies simultaneously, a game is a simultaneous play game. ?But there are games in which one player plays before another player. ?Such games are sequential play games. ?The player who plays first is the leader. The player who plays second is the follower. A Sequential Game Example Player B Player A (U,L) and (D,R) are both Nash equilibria when this game is played simultaneously and we have no way of deciding which equilibrium is more likely to occur. L R U D (3,9) (0,0) (1,8) (2,1) A Sequential Game Example Player B Player A Suppose instead that the game is played sequentially, with A leading and B following. We can rewrite the game in its extensive form. L R U D (3,9) (0,0) (1,8) (2,1) A Sequential Game Example U D L L R R (3,9) (1,8) (0,0) (2,1) A B B A plays first. B plays second. A Sequential Game Example U D L L R R (3,9) (1,8) (0,0) (2,1) A B B A plays first. B plays second. (U,L) is a Nash equilibrium. A Sequential Game Example U D L L R R (3,9) (1,8) (0,0) (2,1) A B B A plays first. B plays second. (U,L) is a Nash equilibrium. (D,R) is a Nash equilibrium. Which is more likely to occur? A Sequential Game Example U D L L R R (3,9) (1,8) (0,0) (2,1) A B B A plays first. B plays second. If A plays U then B plays L。 A gets 3. If A plays D then B plays R。 . 2 5 1 4 2 13 5p p p ppU U U UU? ? ? ? ?? ?( ) ( )/ .(1,2) (0,4) (0,5) (3,2) U,pU D,1pU L,pL R,1pL Player B Mixed Strategies Player A So for there to exist a Nash equilibrium, B must be indifferent between playing Left or Right。 . p p pL L L? ? ? ?3 1 3 4( ) / .(1,2) (0,4) (0,5) (3,2) L, R, U, D, 53524341Player B Mixed Strategies Player B Player A So the game’s only Nash equilibrium has A playing the mixed strategy (3/5, 2/5) and has B playing the mixed strategy (3/4, 1/4). (1,2) (0,4) (0,5) (3,2) U, D, 5352L, R, 43 41Mixed Strategies Player B Player A The payoffs will be (1,2) with probability 3534920? ?(1,2) (0,4) (0,5) (3,2) U, D, L, R, 43 4153529/20 Mixed Strategies Player B Player A The payoffs will be (0,4) with probability 3514320? ?(0,4) (0,5) (3,2) U, D, L, R, 43 415352(1,2) 9/20 3/20 Mixed Strategies Player B Player A The payoffs will be (0,5) with probability 2534620? ?(0,4) (0,5) U, D, L, R, 43 415352(1,2) 9/20 3/20 6/20 (3,2) Mixed Strategies Player B Player A The payoffs will be (3,2) with probability 2514220? ?(0,4) U, D, L, R, 43 415352(1,2) 9/20 3/20 (0,5) (3,2) 6/20 2/20 Mixed Strategies Player B Player A (0,4) U, D, L, R, 43 415352(1,2) 9/20 3/20 (0,5) (3,2) 6/20 2/20 Mixed Strategies Player B Player A A’s expected Nash equilibrium payoff is 1 920 0 320 0 620
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