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Unformatted text preview: Week 5 Game Theory Efficiency and Incentives Two roommates One coffee machine, cost $50 Whether to buy or not? How to share the cost? Is sharing halfhalf efficient? What mechanism can you think of? Game Theory and Applications Game theory helps to model strategic behavior by agents who understand that their actions affect the actions of other agents. 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. 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 games payoff matrix . An Example of a TwoPlayer Game This is the games payoff matrix. Player B Player A Player As payoff is shown first. Player Bs 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 As payoff is 1 and Bs payoff is 8 . This is the games 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 As payoff is 2 and Bs payoff is 1 . This is the games 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 Is (U,R) a likely play?...
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 Fall '09
 Franchsica

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