191T9 - ECON191 (Spring 2009) 20-21.4.2009 (Tutorial 9)...

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1 ECON191 (Spring 2009) 20-21.4.2009 (Tutorial 9) Chapter 9 Introduction to Game Theory (Chapter 13 of textbook) What is game theory? s Game theory is a method for modeling decision making when decisions interact. s 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). s 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 s Games of sequential move : prior moves are observable. b Toshiba observed IBM’s move when Toshiba takes the move. b Toshiba knows which decision node she is on when she has the move. s IBM has 2 strategies: D and U s Toshiba has 2 strategies: D and U s 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 s IBM has 2 strategies: D and U s 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
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2 Dominate strategy and dominated strategy s Dominate strategy: when one strategy is best for a player no matter what strategy the other player uses. b 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. o We will represent the prisoner’s dilemma with normal form. Bob Confess Deny Ann Confess -10, -10 -2, -12 Deny -12, -2 -3, -3 s Is there any dominated strategy for Ann and Bob? s Let’s consider Ann, b If Ann expects Bob to confess , then Ann should confess . (–10 > –12) b If Ann expects Bob to deny , then Ann should confess . (–2 > –3) b Ann gets a higher payoff with confess than deny no matter what she expects Bob to do. b
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This note was uploaded on 10/11/2009 for the course ECON 191 taught by Professor Chen during the Spring '08 term at HKUST.

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191T9 - ECON191 (Spring 2009) 20-21.4.2009 (Tutorial 9)...

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