This preview shows page 1. Sign up to view the full content.
Unformatted text preview: is quasiconcave on A i ; B has a closed graph since each is continuous. Thus by Kakutani's theorem B has a fixed point; as we have noted any fixed point is a Nash equilibrium of the game. Note that this result asserts that a strategic game satisfying certain conditions has at least one Nash equilibrium; as we have seen, a game can have more than one equilibrium. (Results that we do not discuss identify conditions under which a game has a unique Nash equilibrium.) Note also that Proposition 20.3 does not apply to any game in which some player has finitely many actions, since such a game violates the condition that the set of actions of every player be convex. • Exercise 20.4 ( Symmetric games ) Consider a twoperson strategic game that satisfies the conditions of Proposition 20.3. Let N = {1, 2} and assume that the game is symmetric: A 1 = A 2 and if and only if for all and . Use Kakutani's...
View
Full
Document
This note was uploaded on 09/10/2011 for the course DEFR 090234589 taught by Professor Vinh during the Spring '10 term at Aarhus Universitet, Aarhus.
 Spring '10
 VINH

Click to edit the document details