Existence of a pure strategy equilibrium in finite symmetric games where payoff functions are integrally concave

In this paper we show that a finite symmetric game has a pure strategy equilibrium if the payoff functions of players are integrally concave due to Favati and Tardella (1990). Since the payoff functions of any two-strategy game are integrally concave, this generalizes the result of Cheng et al. (2004). A simple algorithm to find a pure strategy equilibrium is also provided.