DP4177 Independence and Heterogeneity in Games of Incomplete Information

Author(s): Robin Mason, Akos Valentinyi
Publication Date: January 2004
Keyword(s): existence, heterogeneity, incomplete information, unique pure strategy equilibrium
JEL(s): C72, D82
Programme Areas: Industrial Organization
Link to this Page: cepr.org/active/publications/discussion_papers/dp.php?dpno=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.