Isotone Equilibrium in Games of Incomplete Information

David McAdams

No 4248-02, Working papers from Massachusetts Institute of Technology (MIT), Sloan School of Management

Abstract: An isotone pure strategy equilibrium exists in any game of incomplete information in which (1) each player i's action set is a finite sublattice of multi-dimensional Euclidean space, (2) types are multidimensional and atomless, and each player's interim expected payoff function satisfies two "non-primitive conditions" whenever others adopt isotone pure strategies: (3) single-crossing in own action and type and (4) quasisupermodularity in own action. Similarly, given that (134) and (2') types are multi-dimensional (with atoms) an isotone mixed strategy equilibrium exists. Conditions (34) are satisfied in supermodular and log-supermodular games given affiliated types, and in games with independent types in which each player's ex post payoff satisfies (a) supermodularity in own action and (b) non-decreasing differences in own action and type. These results also extend to games with a continuum action space when each player's ex post payoff is also continuous in his and others' actions.

Keywords: Equilibrium; Isotone (search for similar items in EconPapers)
Date: 2002-08-09
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Citations: View citations in EconPapers (2)

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