Independence and Heterogeneity in Games of Incomplete Information
Robin A. Mason
University of Southampton - Division of Economics; Centre for Economic Policy Research (CEPR)
Cardiff Business School; Centre for Economic Policy Research (CEPR)
CEPR Discussion Paper No. 4177
This Paper provides a sufficient condition for the existence and uniqueness of equilibrium in monotone pure strategies, in games of incomplete information. First, we show that if each player's incremental ex post pay-off 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 pay-off 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.
Number of Pages in PDF File: 50
Keywords: Incomplete information, heterogeneity, existence, unique pure strategy equilibrium
JEL Classification: C72, D82
Date posted: January 20, 2004
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