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Independence and Heterogeneity in Games of Incomplete Information ∗

By Robin Mason and Ákos Valentinyi

Abstract

This paper provides a sufficient condition for existence and uniqueness of equilibrium, which is in monotone pure strategies, in games of incomplete information. First, we show that if each player’s incremental ex post payoff is uniformly increasing in its own action and type, and its type is sufficiently uninformative of the types of its opponents (independence), then its expected payoff satisfies a strict single crossing property in its own action and type, for any strategy profile played by its opponents. This ensures that a player’s best response to any strategy profile is a monotone pure strategy. Secondly, we show that if, in addition, there is sufficient heterogeneity of the conditional density of types, then the best response correspondence is a contraction mapping. This ensures equilibrium existence and uniqueness. Our approach allows us to establish these results in a wide range of applications, including cases where there are no existing existence results

Topics: Incomplete Information, Heterogeneity, Existence, Unique pure strategy equilibrium
Year: 2003
OAI identifier: oai:CiteSeerX.psu:10.1.1.203.175
Provided by: CiteSeerX
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