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Journal Articles

Characterizations of the Existence of Equilibria in Games with Discontinuous and Nonquasiconcave Payoffs

1993, Review of Economic Studies

Michael R. Baye, Guoqiang Tian, Jianxian Zhou

Abstract

This paper characterizes pure-strategy and dominant-strategy Nash equilibrium in noncooperative games that may have discontinuous and/or non-quasi-concave payoffs. Conditions called diagonal transfer quasi-concavity and uniform transfer quasi-concavity are shown to be necessary and, with conditions called diagonal transfer continuity and transfer upper semicontinuity, sufficient for the existence of pure-strategy and dominant-strategy Nash equilibrium, respectively. The results are used to examine the existence or nonexistence of equilibrium in some well-known economic games with discontinuous and/or non-quasi-concave payoffs. Copyright 1993 by The Review of Economic Studies Limited.

Citation

Michael R. Baye, Guoqiang Tian, and Jianxin Zhou, “Characterizations of the Existence of Equilibria in Games with Discontinuous and Nonquasiconcave Payoffs,” Review of Economic Studies, Vol. 60 (October 1993), pp. 935-948.