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Independence and heterogeneity in games of incomplete information

Independence and heterogeneity in games of incomplete information
Independence and heterogeneity in games of incomplete information
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. In contrast to existing results, our uniqueness result does not rely on strategic complementarities; this allows for a wider range of applications.
incomplete information, heterogeneity, existence, unique pure strategy equilibrium
307
University of Southampton
Mason, Robin
c989f0e0-de54-495d-aeaf-75b42d62cb61
Valentinyi, Akos
7519c19b-8434-4ba2-88a6-ae066471ffcf
Mason, Robin
c989f0e0-de54-495d-aeaf-75b42d62cb61
Valentinyi, Akos
7519c19b-8434-4ba2-88a6-ae066471ffcf

Mason, Robin and Valentinyi, Akos (2003) Independence and heterogeneity in games of incomplete information (Discussion Papers in Economics and Econometrics, 307) Southampton, GB. University of Southampton

Record type: Monograph (Discussion Paper)

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. In contrast to existing results, our uniqueness result does not rely on strategic complementarities; this allows for a wider range of applications.

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Published date: July 2003
Additional Information: JEL classification: C72; D82
Keywords: incomplete information, heterogeneity, existence, unique pure strategy equilibrium

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Local EPrints ID: 167733
URI: https://eprints.soton.ac.uk/id/eprint/167733
PURE UUID: 09eebad5-1a08-4d7c-a6a9-63899fce8eb0

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Date deposited: 17 Nov 2010 11:30
Last modified: 18 Jul 2017 12:23

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