Nash equilibrium with Sugeno payoff

TL;DR

This paper investigates Nash equilibria in games where payoffs are modeled by Sugeno integrals, extending previous work on capacities and Choquet integrals, and proves their existence using advanced mathematical methods.

Contribution

It introduces the existence of Nash equilibria for games with Sugeno integral payoffs, employing categorical and convexity theories, which is a novel approach in this context.

Findings

Existence of Nash equilibrium for games with Sugeno payoffs proven.

Utilizes categorical methods and abstract convexity theory.

Extends prior work on capacities and Choquet integrals.

Abstract

This paper is devoted to Nash equilibrium for games in capacities. Such games with payoff expressed by Choquet integral were considered by Kozhan and Zarichnyi (Nash equilibria for games in capacities, Econ. Theory {\bf 35} (2008) 321--331) and existence of Nash equilibrium was proved. We also consider games in capacities but with expected payoff expressed by Sugeno integral. We prove existence of Nash equilibrium using categorical methods and abstract convexity theory.