微觀經(jīng)濟(jì)學(xué)趙耀輝第28章(已修改)
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【正文】 Chapter TwentyEight Game Theory 博弈論 Contents ?Dominant strategy ?Nash equilibrium ?Prisoner’s dilemma and repeated games ?Multiple equilibria and sequential games ?Pure and mixed strategies Game Theory ?Game theory models strategic behavior by agents who understand that their actions affect the actions of other agents. Some Applications of Game Theory ?The study of oligopolies (industries containing only a few firms) ?The study of cartels。 . OPEC ?The study of externalities。 . 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) (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。 ?In the “strength is weakness” example, (W,P) is a Nash equilibrium. ?In the “battle of sexes” example, there are two Nash equilibria. The Prisoner’s Dilemma ?A Nash equilibrium may not be Pareto optimal/efficient. ?Consider a famous second example of a twoplayer game called the Prisoner’s
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