Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs

This paper characterizes pure-strategy and dominant-strategy Nash equilibrium in non cooperative games which 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 semi continuity, 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-quasi concave 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 quasi concave-not the failure of payoffs to be quasi concave, as has been elsewhere conjectured. 1993 The Review of Economic Studies Limited.

Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs Academic Article