微觀經(jīng)濟(jì)學(xué)（趙耀輝）第28章-全文預(yù)覽
【正文】 does have a Nash equilibrium in mixed strategies. How is it puted? (1,2) (0,4) (0,5) (3,2) U D L R Player B Mixed Strategies Player A (1,2) (0,4) (0,5) (3,2) U,pU D,1pU L,pL R,1pL Player B Mixed Strategies Player A If B plays Left her expected payoff is 2 5 1p pU U? ?( )(1,2) (0,4) (0,5) (3,2) U,pU D,1pU L,pL R,1pL Player B Mixed Strategies Player A If B plays Left her expected payoff is If B plays Right her expected payoff is 2 5 1p pU U? ?( ).4 2 1p pU U? ?( ).(1,2) (0,4) (0,5) (3,2) U,pU D,1pU L,pL R,1pL Player B Mixed Strategies Player A 2 5 1 4 2 1p p p pU U U U? ? ? ? ?( ) ( )If then B would play only Left. But there are no Nash equilibria in which B plays only Left. (1,2) (0,4) (0,5) (3,2) U,pU D,1pU L,pL R,1pL Player B Mixed Strategies Player A 2 5 1 4 2 1p p p pU U U U? ? ? ? ?( ) ( )If then B would play only Right. But there are no Nash equilibria in which B plays only Right. (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。 A gets 3. If A plays D then B plays R。 . using a mon resource such as a fishery. ?The study of military strategies. What is a Game? ?A game consists of –a set of players –a set of strategies for each player –the payoffs to each player for every possible list of strategy choices by the players. TwoPlayer Games ?A game with just two players is a twoplayer game. ?We will study only games in which there are two players, each of whom can choose between only two strategies. An Example of a TwoPlayer Game ?The players are called A and B. ?Player A has two strategies, called “Up” and “Down”. ?Player B has two strategies, called “Left” and “Right”. ?The table showing the payoffs to both players for each of the four possible strategy binations is the game’s payoff matrix (支付矩陣 ). An Example of a TwoPlayer Game A play of the game is a pair such as (U,R) where the 1st element is the strategy chosen by Player A and the 2nd is the strategy chosen by Player B. Player B Player A L R U D (1,2) (2,1) (0,1) (1,0) An Example of a TwoPlayer Game What plays are we likely to see for this game? Player B Player A L R U D (1,2) (2,1) (0,1) (1,0) An Example of a TwoPlayer Game If B plays Left then A’s best reply is Down. Player B Player A L R U D (1,2) (2,1) (0,1) (1,0) An Example of a TwoPlayer Game If B plays Right then A’s best reply is Down. Player B Player A L R U D (1,2) (2,1) (0,1) (1,0) An Example of a TwoPlayer Game So no matter what B plays, A’s best reply is always Down. Down is A’s dominant strategy （ 超優(yōu) 策略） . Player B Player A L R U D (1,2) (2,1) (0,1) (1,0) An Example of a TwoPlayer Game Similarly, Left is B’s dominant strategy. Player B Player A L R U D (1,2) (2,1) (0,1) (1,0) An Example of a TwoPlayer Game Therefore, (Down, Left) is dominant strategy for both players. It is the only equilibrium. Player B Player A L R U D (1,2) (2,1) (0,1
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