Isotone Equilibrium in Games of Incomplete Information

Posted: 14 Jan 2008

See all articles by David McAdams

David McAdams

Massachusetts Institute of Technology (MIT) - Economics, Finance, Accounting (EFA)

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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.

Suggested Citation

McAdams, David, Isotone Equilibrium in Games of Incomplete Information. Econometrica Vol. 71, No. 4, July 2003; MIT Sloan Working Paper No. 4248-02. Available at SSRN: https://ssrn.com/abstract=1083692 or http://dx.doi.org/10.2139/ssrn.317979

David McAdams (Contact Author)

Massachusetts Institute of Technology (MIT) - Economics, Finance, Accounting (EFA) ( email )

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