lecture15 - Lecture XV: Games with Incomplete Information...

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Lecture XV: Games with Incomplete Information Markus M. M¨obius April 28, 2004 Gibbons, chapter 3 Osborne, chapter 9 1 Introduction Informally, a game with incomplete information is a game where the game being played is not common knowledge. This idea is tremendously important in practice where its almost always a good idea to assume that something about the game is unknown to some players. What could be unknown? 1. Payoffs: In a price or quantity competition model you may know that your rival maximizes profits but now what his costs are (and hence his profits). 2. Identity of other players: else will come up with the same drug? 3. What moves are possible: What levels of quality can rivals in a quality competition choose? 4. How does the outcome depend on action: Workers work/shirk don’t know probability of getting caught because product fails. 1
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2 Examples 2.1 Example I: Crazy Incumbent Think of a standard entry game where the incumbent is ’crazy’ with proba- bility 1 - p and rational with probability p . The normal incumbent faces the standard entry game from lecture 11: 2 In Out 1 F A 2 0 -1 -1 1 1 If the incumbent is crazy he will always want to fight because is is facing a different subgame: 2 In Out 1 F A 2 0 1 -1 -1 1 2
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2.2 Example II: Auction Two bidders are trying to purchase the same item at a sealed bid auction. The players simultaneously choose b 1 and b 2 and the good is sold to the highest bidder at his bid price (assume coin flip if b 1 = b 2 ). Suppose that the players’ utilities are u i ( b i ,b - i ) = v i - b i if b i > b - i 1 2 ( v i - b i ) if b i = b - i 0 if b i < b - i The crucial incomplete information is that while each player knows his own valuation, he does not know his rival’s. Assume, each has a prior that his rival’s valuation is uniform on [0 , 1] and that this is common knowledge. 2.3 Example III: Public Good
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This note was uploaded on 05/19/2010 for the course DFDAS 220 taught by Professor Ding during the Fall '10 term at Academy of Art University.

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lecture15 - Lecture XV: Games with Incomplete Information...

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