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Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-Quasiconcave Payoffs
Michael R. Baye, Guoqiang Tian and Jianxin Zhou
The Review of Economic Studies
Vol. 60, No. 4 (Oct., 1993), pp. 935-948
Published by: Oxford University Press
Stable URL: http://www.jstor.org/stable/2298107
Page Count: 14
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This paper characterizes pure-strategy and dominant-strategy Nash equilibrium in non-cooperative games which may have discontinuous and/or non-quasiconcave payoffs. Conditions called diagonal transfer quasiconcavity and uniform transfer quasiconcavity 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 non-existence of equilibrium in some well-known economic games with discontinuous and/or non-quasiconcave payoffs. For example, we show that the failure of the existence of a pure-strategy Nash equilibrium in the Hotelling model is due to the failure of an aggregator function to be diagonal transfer quasiconcave-not the failure of payoffs to be quasiconcave, as has been elsewhere conjectured.
The Review of Economic Studies © 1993 The Review of Economic Studies, Ltd.