n6 - Economics 405/505 Introduction to Game Theory Prof....

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Unformatted text preview: Economics 405/505 Introduction to Game Theory Prof. Rui Zhao Static Games with Incomplete Information 1. Structure of Games with Incomplete Information In a game with incomplete information, before the game starts some (or all) players already have some information that is not known to the other players. A player’s private information can be anything about how the game will be played. Here, we consider games with the following structure: • A set of players • Private information: each player has some information about the state of the game that is not known to other players; the same player having different information will be referred to as different types of the player. • Actions: each player has a set of actions. • Beliefs: each player has a belief about the likelihood of the types of other players. • Payoffs: each player’s payoff depends on all players’ actions and his own type. 2. Example: Battle of the Sexes Two players. Each has two actions: Football (F), Concert (C). Player 2’s payoff depends on her type : if she wants to meet player 1 then her payoff is higher if both players choose the same action; if she wants to avoid player 1 then her payoff is higher if they choose different actions. Player 2 knows her own type, but player 1 does not — in this case we say player 2 has private information . Player 1 has a belief: he assigns probability p to player 2 being type “Meet” and probability 1- p to type “Avoid”. The situations are represented by the following matrices, with player 1 choosing rows. Meet Avoid p 1- p F C F C F (2, 1) (0, 0) (2, 0) (0, 2) C (0, 0) (1, 2) (0, 1) (1, 0) Assume p = 1 / 2 . What is an equilibrium in this game? First of all, in this game a strategy of player 1 is simply an action, either F or C, but a strategy of player 2 should be a pair of actions, one for each type of player 2. For example, player 2’s strategy might be (choosing F if type = Meet, choosing C if type = Avoid); we denote the stragey by the 1 ordered pair ( F,C ). We claim player 1 choosing F , player 2 choosing F if her type is Meet and player 2 choosing C if her type is...
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This note was uploaded on 09/14/2011 for the course ECON 505 taught by Professor Zhao during the Spring '11 term at SUNY Albany.

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n6 - Economics 405/505 Introduction to Game Theory Prof....

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