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Unformatted text preview: 10/5/2010 1 1 Game Theory Chapter 28 Game Theory Game theory helps to model 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. Bargaining. How markets work. 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 choice of strategies 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 actions. An Example of a TwoPlayer Game The players are called A and B. Player A has two actions, called “Up” and “Down”. Player B has two actions, called “Left” and “Right”. The table showing the payoffs to both players for each of the four possible action combinations is the game’s payoff matrix . 10/5/2010 2 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 A play of the game is a pair such as (U,R) where the 1st element is the action chosen by Player A and the 2nd is the action chosen by Player B. L R U D (3,9) (0,0) (1,8) (2,1) Player B Player A 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. L R U D (3,9) (0,0) ( 1 , 8 ) (2,1) Player B Player A 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. L R U D (3,9) (0,0) (1,8) ( 2 , 1 ) Player B Player A An Example of a TwoPlayer Game What plays are we likely to see for this game? L R U D (3,9) (0,0) (1,8) (2,1) Player B Player A An Example of a TwoPlayer Game 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. L R U D (3,9) (0,0) ( 1 , 8 ) (2,1) Is (U,R) a likely play? Player B Player A 10/5/2010 3 An Example of a TwoPlayer Game If B plays Right then A’s best reply is Down. If A plays Down then B’s best reply is Right. So (D,R) is a likely play. L R U D (3,9) (0,0) (1,8) ( 2 , 1 ) Is (D,R) a likely play? Player B Player A An Example of a TwoPlayer Game If A plays Down then B’s best reply is Right, so (D,L) is not a likely play....
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This note was uploaded on 06/12/2011 for the course ECONOMICS 3291 taught by Professor Professorsnamespublishedtheyarethesoleowners during the Three '11 term at University of New South Wales.
 Three '11
 professorsnamespublishedtheyarethesoleowners
 Economics, Game Theory

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