Independence and Heterogeneity in Games of Incomplete Information

50 Pages Posted: 20 Jan 2004  

Robin A. Mason

University of Southampton - Division of Economics; Centre for Economic Policy Research (CEPR)

Akos Valentinyi

Cardiff Business School; Centre for Economic Policy Research (CEPR)

Date Written: January 2004

Abstract

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.

Keywords: Incomplete information, heterogeneity, existence, unique pure strategy equilibrium

JEL Classification: C72, D82

Suggested Citation

Mason, Robin A. and Valentinyi, Akos, Independence and Heterogeneity in Games of Incomplete Information (January 2004). CEPR Discussion Paper No. 4177. Available at SSRN: https://ssrn.com/abstract=490702

Robin Mason (Contact Author)

University of Southampton - Division of Economics ( email )

Southampton, SO17 1BJ
United Kingdom
+44 23 8059 3268 (Phone)
+44 23 8059 3858 (Fax)

Centre for Economic Policy Research (CEPR)

77 Bastwick Street
London, EC1V 3PZ
United Kingdom

Akos Valentinyi

Cardiff Business School ( email )

Cardiff, CF10 3EU
United Kingdom

Centre for Economic Policy Research (CEPR)

77 Bastwick Street
London, EC1V 3PZ
United Kingdom

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