Chapter Twenty-Eight Game Theory
Chapter Twenty-Eight Game Theory
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 strategies
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
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
An Example of a Two-Player Game Player B R U (3,9) (1,8) This is the Player A game's D (0,0) (2,1) payoff matrix. Player A's payoff is shown first. Player B's payoff is shown second
An Example of a Two-Player Game This is the game’s payoff matrix. Player B Player A Player A’s payoff is shown first. Player B’s payoff is shown second. L R U D (3,9) (0,0) (1,8) (2,1)
An Example of a Two-Player Game Player B R U (3,9) （1,8) This is the Player A game's (0,0)(2,1) payoff matrix. E.g.if A plays Up and B plays Right then A's payoff is 1 and B's payoff is 8
An Example of a Two-Player Game E.g. if A plays Up and B plays Right then A’s payoff is 1 and B’s payoff is 8. This is the game’s payoff matrix. Player B Player A L R U D (3,9) (0,0) (1,8) (2,1)
An Example of a Two-Player Game Player B L R U (3,9)(1,8) This is the Player A game's D (0,0)(2,1） payoff matrix. And if A plays Down and B plays Right then A's payoff is 2 and B's payoff is 1
An Example of a Two-Player Game And if A plays Down and B plays Right then A’s payoff is 2 and B’s payoff is 1. This is the game’s payoff matrix. Player B Player A L R U D (3,9) (0,0) (1,8) (2,1)
An Example of a Two-Player Game Player B R U (3,9)(1,8) Player A D (0,0)(2,1) 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 Player B Player A 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. L R U D (3,9) (0,0) (1,8) (2,1)