北京大学：《微观经济学》Chapter Twenty-Eight Game Theory 博弈论

Chapter twenty-Eight Game Theory 博弈论

Chapter Twenty-Eight Game Theory 博弈论

Contents Dominant strategy Nash equilibrium Prisoner's dilemma and repeated games Multiple equilibria and sequential games Pure and mixed strategies

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

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; e.g. OPEC The study of externalities; e.g. using a common resource such as a fishery. The study of military strategies

Some Applications of Game Theory The study of oligopolies (industries containing only a few firms) The study of cartels; e.g. OPEC The study of externalities; e.g. using a common 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

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

Two-Player Games a game with just two players is a two-player game We will study only games in which there are two players, each of whom can choose between only two strateqies

Two-Player Games A game with just two players is a two-player 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 two-Player 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 combinations is the game' s payoff matrix(支付矩阵

An Example of a Two-Player 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 combinations is the game’s payoff matrix (支付矩阵)

An Example of a Two-Player Game Player B R U(12)(0,1) Player A D(2,1)(1,0) 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

An Example of a Two-Player 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 Two-Player Game Player B R U(12)(0,1) Player A D(2,1)(1,0) What plays are we likely to see for this game

An Example of a Two-Player 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 two-Player Game Player B R U(12)(0,1) Player A D(2,1)(1,0) If B plays Left then A's best reply is Down

An Example of a Two-Player 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)