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Independence and Heterogeneity in Games of Incomplete Information

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  • Valentinyi, Akos
  • Mason, Robin

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.

Suggested Citation

  • Valentinyi, Akos & Mason, Robin, 2004. "Independence and Heterogeneity in Games of Incomplete Information," CEPR Discussion Papers 4177, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:4177
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    References listed on IDEAS

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    Cited by:

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    More about this item

    Keywords

    Incomplete information; Heterogeneity; Existence; Unique pure strategy equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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