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.
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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number
4177.
Find related papers by JEL classification: C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information
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Carlsson, Hans & van Damme, Eric, 1993.
"Global Games and Equilibrium Selection,"
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Edward L. Glaeser & Jose Scheinkman, 2000.
"Non-Market Interactions,"
NBER Working Papers
8053, National Bureau of Economic Research, Inc.
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