191T7 - ECON191 (Spring 2010) 15, 16 & 19.4.2010 (Tutorial...

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1 ECON191 (Spring 2010) 15, 16 & 19.4.2010 (Tutorial 7) Chapter 9 Introduction to Game Theory (Chapter 13 of textbook) What is game theory? Game theory is a method for modeling decision making when decisions interact. A game is characterized by (i) The set of players (ii) The strategy set (the set of feasible actions) - A strategy is a complete plan of action , which tells the player what to do every time where he has the move. (iii) The payoffs of the players - Payoff of a player depends not only on his own strategy, but also the strategy of the other player (interdependence). In game theory, we assume players are rational and they are only interested in their own payoffs. Representation of games (1) Extensive form (Game tree/Kuhn tree) - Decision nodes : represents points in the game where a player takes an action. - Braches at each decision node: represents the alternative actions that the player with move can take. - Terminal nodes : represents the final outcome of the game. Associated with each terminal node is a payoff for every player. (2) Strategic from - Payoff matrices IBM has 2 strategies: D and U Toshiba has 2 strategies: D and U Toshiba DOS UNIX IBM DOS 600, 200 100, 100 UNIX 100, 100 200, 600 IBM’s payoff Toshiba’s payoff Games of sequential move : prior moves are observable. Toshiba observed IBM’s move when Toshiba takes the move. Toshiba knows which decision node she is on when she has the move. IBM has 2 strategies: D and U Toshiba has 2 strategies: D and U First mover advantage UNIX DOS UNIX DOS UNIX DOS 600 200 100 100 100 100 200 600 IBM TOSHIBA TOSHIBA IBM’s payoff Toshiba’s payoff
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2 Dominate strategy and dominated strategy Dominate strategy: when one strategy is best for a player no matter what strategy the other player uses. We will explain these concepts with the classic example of Prisoner’s Dilemma. Example : Prisoner’s Dilemma The story: Ann and Bob have been caught stealing a car. The police suspect that they have also robbed the bank, a more serious crime. The police has no evidence for the robbery, and needs at least one person to confess to get a conviction. Ann and Bob are separated and each told: (i) If each confesses, then each will get a 10 year sentence. (ii) If one confesses, but the other denies, then he will get 2 year and his accomplice will get 12 yrs. (iii) If neither confesses, then each will get a 3 year sentence for auto theft. We will represent the prisoner’s dilemma with normal form. Bob Confess Deny Ann Confess -10, -10 -2, -12 Deny -12, -2 -3, -3 Is there any dominated strategy for Ann and Bob? Let’s consider Ann, If Ann expects Bob to confess , then Ann should confess . (–10 –12) If Ann expects Bob to deny , then Ann should confess . (–2 –3) Ann gets a higher payoff with confess than deny no matter what she expects Bob to do. If Ann is rational, she will
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This note was uploaded on 08/26/2010 for the course ECON ECON191 taught by Professor Chan during the Spring '09 term at HKUST.

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191T7 - ECON191 (Spring 2010) 15, 16 & 19.4.2010 (Tutorial...

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