Nash equilibrium for binary convexities

Abstract

This paper is devoted to Nash equilibrium for games in capacities. Such games with payoff expressed by the Choquet integral were considered by Kozhan and Zarichnyi (2008) and existence of Nash equilibrium was proved. We also consider games in capacities but with expected payoff expressed by the Sugeno integral. We prove existence of Nash equilibrium in a general context of abstract binary (non-linear) convexity and then we obtain an existence theorem for games in capacities.