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Unformatted text preview: 6.207/14.15: Networks Lectures 1921: Incomplete Information: Bayesian Nash Equilibria, Auctions and Introduction to Social Learning Daron Acemoglu and Asu Ozdaglar MIT November 23, 25 and 30, 2009 1 Networks: Lectures 2022 Introduction Outline Incomplete information. Bayes rule and Bayesian inference. Bayesian Nash Equilibria. Auctions. Extensive form games of incomplete information. Perfect Bayesian (Nash) Equilibria. Introduction to social learning and herding. Reading: Osborne, Chapter 9. EK, Chapter 16. 2 Networks: Lectures 2022 Incomplete Information Incomplete Information In many game theoretic situations, one agent is unsure about the preferences or intentions of others. Incomplete information introduces additional strategic interactions and also raises questions related to “learning”. Examples: Bargaining (how much the other party is willing to pay is generally unknown to you) Auctions (how much should you be for an object that you want, knowing that others will also compete against you?) Market competition (firms generally do not know the exact cost of their competitors) Signaling games (how should you infer the information of others from the signals they send) Social learning (how can you leverage the decisions of others in order to make better decisions) 3 Networks: Lectures 2022 Incomplete Information Example: Incomplete Information Battle of the Sexes Recall the battle of the sexes game, which was a complete information “coordination” game. Both parties want to meet, but they have different preferences on “Ballet” and “Football”. B F B (2 , 1) (0 , 0) F (0 , 0) (1 , 2) In this game there are two pure strategy equilibria (one of them better for player 1 and the other one better for player 2), and a mixed strategy equilibrium. Now imagine that player 1 does not know whether player 2 wishes to meet or wishes to avoid player 1. Therefore, this is a situation of incomplete information —also sometimes called asymmetric information . 4 Networks: Lectures 2022 Incomplete Information Example (continued) We represent this by thinking of player 2 having two different types , one type that wishes to meet player 1 and the other wishes to avoid him. More explicitly, suppose that these two types have probability 1/2 each. Then the game takes the form one of the following two with probability 1/2. B F B (2 , 1) (0 , 0) F (0 , 0) (1 , 2) B F B (2 , 0) (0 , 2) F (0 , 1) (1 , 0) Crucially, player 2 knows which game it is (she knows the state of the world ), but player 1 does not. What are strategies in this game? 5 Networks: Lectures 2022 Incomplete Information Example (continued) Most importantly, from player 1’s point of view, player 2 has two possible types (or equivalently, the world has two possible states each with 1/2 probability and only player 2 knows the actual state)....
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 Fall '09
 Acemoglu
 Game Theory, incomplete information, payoﬀs

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