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

This preview shows pages 1–4. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 8

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online