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Unformatted text preview: Chapter TwentyEight Game Theory 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. 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 combinations is the game’s payoff matrix . An Example of a TwoPlayer 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 TwoPlayer Game E.g. if A plays U p and B plays R ight 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 TwoPlayer Game And if A plays D own and B plays R ight 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 TwoPlayer 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) An Example of a TwoPlayer Game What plays are we likely to see for this game? Player B Player A L R U D (3,9) (0,0) (1,8) (2,1) An Example of a TwoPlayer Game Player B Player A Is (U,R) a likely play? L R U D (3,9) (0,0) ( 1 , 8 ) (2,1) An Example of a TwoPlayer Game Player B Player A If B plays Right then A’s best reply is Down since this improves A’s payoff from 1 to 2. So (U,R) is not a likely play. Is (U,R) a likely play? L R U D (3,9) (0,0) ( 1 , 8 ) (2,1) An Example of a TwoPlayer Game Player B Player A Is (D,R) a likely play? L R U D (3,9) (0,0) (1,8) ( 2 , 1 ) An Example of a TwoPlayer Game Player B Player A Is (D,R) a likely play? If B plays Right then A’s best reply is Down. L R U D (3,9) (0,0) (1,8) ( 2 , 1 ) An Example of a TwoPlayer Game Player B Player A If B plays Right then A’s best reply is Down....
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This note was uploaded on 01/06/2012 for the course ECON 102 taught by Professor Goodhart during the Spring '11 term at Abu Dhabi University.
 Spring '11
 GOODHART
 Game Theory

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