Isotone Equilibrium in Games of Incomplete Information
Name
Isotone Equilibrium in Games 4248-02 .pdf
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338.92 KB
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Checksum (MD5)
372be5114ec758dbccee6184630fcf98
Author(s)
McAdams, David
Date Issued
August 9, 2002
Series/Report no.
MIT Sloan School of Management Working Paper;4248-02
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.
Subjects
Equilibrium
Isotone
Persistent DSpace Link
