微觀經(jīng)濟(jì)學(xué)趙耀輝第28章(存儲(chǔ)版)
【正文】 for both players. It is the only equilibrium. Player B Player A L R U D (1,2) (2,1) (0,1) (1,0) No Dominant Strategy for One Player When Strength Is Weakness 大豬 小豬 P W P W (1,10) (6,4) (1,10) (0,0) No Dominant Strategy for Both The Battle of Sexes 小紅 小東 C S C S (2,1) (0,0) (0,0) (1,2) Nash Equilibrium ? A play of the game where each strategy is a best reply to the other is a Nash equilibrium. ? A dominant strategy equilibrium is a Nash equilibrium。 that is, as playing purely one or the other. ? The strategies presented so far are players’ pure strategies （ 純粹策略） . ? Consequently, equilibria are pure strategy Nash equilibria. ? Must every game have at least one pure strategy Nash equilibrium? Pure Strategies Player B Player A Here is a new game. Are there any pure strategy Nash equilibria? (1,2) (0,4) (0,5) (3,2) U D L R Pure Strategies Player B Player A Is (U,L) a Nash equilibrium? (1,2) (0,4) (0,5) (3,2) U D L R Pure Strategies Player B Player A Is (U,L) a Nash equilibrium? No. Is (U,R) a Nash equilibrium? (1,2) (0,4) (0,5) (3,2) U D L R Pure Strategies Player B Player A Is (U,L) a Nash equilibrium? No. Is (U,R) a Nash equilibrium? No. Is (D,L) a Nash equilibrium? (1,2) (0,4) (0,5) (3,2) U D L R Pure Strategies Player B Player A Is (U,L) a Nash equilibrium? No. Is (U,R) a Nash equilibrium? No. Is (D,L) a Nash equilibrium? No. Is (D,R) a Nash equilibrium? (1,2) (0,4) (0,5) (3,2) U D L R Pure Strategies Player B Player A Is (U,L) a Nash equilibrium? No. Is (U,R) a Nash equilibrium? No. Is (D,L) a Nash equilibrium? No. Is (D,R) a Nash equilibrium? No. (1,2) (0,4) (0,5) (3,2) U D L R More Examples Matching Pennies Player B Player A (1,1) (1, 1) (1,1) (1, 1) H T H T More Examples 點(diǎn)球 進(jìn)攻球員 守門員 (1,0) (0, 1) (0,1) (1, 0) 左 右 左 右 Pure Strategies Player B Player A So the game has no Nash equilibria in pure strategies. Even so, the game does have a Nash equilibrium, but in mixed strategies (混合策略 ). (1,2) (0,4) (0,5) (3,2) U D L R Mixed Strategies ?Instead of playing purely Up or Down, Player A selects a probability distribution (pU,1pU), meaning that with probability pU Player A will play Up and with probability 1pU will play Down. ?Player A is mixing over the pure strategies Up and Down. ?The probability distribution (pU,1pU) is a mixed strategy for Player A. Mixed Strategies ?Similarly, Player B selects a probability distribution (pL,1pL), meaning that with probability pL Player B will play Left and with probability 1pL will play Right. ?Player B is mixing over the pure strategies Left and Right. ?The probability distribution (pL,1pL) is a mixed strategy for Player B. Mixed Strategies Player A This game has no pure strategy Nash equilibria but it 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
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