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

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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? square4 Game theory is a method for modeling decision making when decisions interact. square4 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). square4 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 square4 Games of sequential move : prior moves are observable. bright Toshiba observed IBM’s move when Toshiba takes the move. bright Toshiba knows which decision node she is on when she has the move. square4 IBM has 2 strategies: D and U square4 Toshiba has 2 strategies: D and U square4 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 square4 IBM has 2 strategies: D and U square4 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 square4 Dominate strategy: when one strategy is best for a player no matter what strategy the other player uses. bright 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. orightshadlft We will represent the prisoner’s dilemma with normal form. Bob Confess Deny Ann Confess -10, -10 -2, -12 Deny -12, -2 -3, -3 square4 Is there any dominated strategy for Ann and Bob? square4 Let’s consider Ann, bright If Ann expects Bob to confess , then Ann should confess . (–10 > –12) bright If Ann expects Bob to deny , then Ann should confess . (–2 > –3) bright Ann gets a higher payoff with confess than deny no matter what she expects Bob to do.
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191T9 - ECON191(Spring 2009 20-21.4.2009(Tutorial 9 Chapter...

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