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

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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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