5.GameTheory

5.GameTheory - Game Theory Outline Normal form games...

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Game Theory Outline ± Normal form games ( simultaneous ), Nash equilibrium ± Extensive form games ( sequential), Subgame perfect equilibrium ± Repeated games ± Game theory analyzes the interactions between rational, decision-making individuals who may not be able to predict fully the outcomes of their decision. ± Models of oligopoly can be viewed as games of strategies or actions (such as setting output, price, or advertising levels). Two representations of game ± Normal form game(simultaneous move games): Simultaneous in the sense that when one player chooses his action the action taken by the other player(s) unknown. (Not necessary that players move at same point in time) ± Extensive form game (sequential move games): Sequential in the sense that before one player moves he observes the action chosen by other player(s). Normal Form Games Three elements: ± A set of players I = {1,2,…, N } ± Each Player’s action set A i = { a i 1 ,a i 2 ,… } e.g., if the firm chooses price, the action set is any price greater than zero. outcome : a = ( a 1 , a 2 ,…,a i ,…, a N , ) ± Each player’s payoff function π i ( a ), i.e. payoff as a result of the actions by all the agents. e.g., firm’s profit Extensive Example: Prisoner’s Dilemma Jerry -1 -1 -9 0 Silent 0 -9 -5 -5 Confess Silent Confess Tom Example: Prisoner’s Dilemma (cont’d) Jerry -1 -1 -9 0 Silent 0 -9 -5 -5 Confess Silent Confess Best response of a player i for a given
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5.GameTheory - Game Theory Outline Normal form games...

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