Games in possibility capacities with payoff expressed by fuzzy integral

TL;DR

This paper explores non-cooperative games with players using fuzzy integral-based strategies, analyzing the existence of Nash equilibria and highlighting differences between Sugeno and Choquet integrals.

Contribution

It introduces the analysis of Nash equilibrium existence in games with fuzzy integral payoffs, showing positive results for Sugeno integrals and limitations for Choquet integrals.

Findings

Nash equilibrium exists for games with Sugeno integral payoffs.

Choquet integral payoffs can lack Nash equilibrium, indicating limitations.

Fuzzy integrals based on maximum operations are more suitable for possibility capacities.

Abstract

This paper studies non-cooperative games where players are allowed to play their mixed non-additive strategies. Expected payoffs are expressed by so-called fuzzy integrals: Choquet integral, Sugeno integral and generalizations of Sugeno integral obtained by using triangular norms. We consider the existence problem of Nash equilibrium for such games. Positive results for Sugeno integral and its generalizations are obtained. However we provide some example of a game with Choquet payoffs which have no Nash equilibrium. Such example demonstrates that fuzzy integrals based on the maximum operation are more suitable for possibility capacities then Choquet integral which is based on the addition operation.