Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs
刻画了非合作博弈中纯策略和占优策略纳什均衡的存在条件，引入了对角转移拟凹性和均匀转移拟凹性等概念，并应用于分析Hotelling模型等经典经济博弈的均衡存在性。
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.