On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games

Philip Reny ()

Econometrica, 1999, vol. 67, issue 5, 1029-1056

Abstract: A game is better-reply secure if for every non equilibrium strategy x* and every payoff vector limit u* resulting from strategies approaching x*, some player i has a strategy yielding a payoff strictly above u[subscript i superscript *] even if the others deviate slightly from x*. If strategy spaces are compact and convex, payoffs are quasiconcave in the owner's strategy, and the game is better-reply secure, then a pure strategy Nash equilibrium exists. Better-reply security holds in many economic games. It also permits new results on the existence of symmetric and mixed strategy equilibria.

Date: 1999
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