A Metaheuristic Approach to Compute Pure Nash Equilibria

Abstract

A pure Nash equilibrium is a famous concept in the field of game theory and has a wide range of applications. In the last decade, a lot of progress has been made in determining the computational complexity of finding equilibria in games. Deciding if a pure Nash equilibrium exists in n-player normal form games and several subclasses has been shown to be NP-complete. Current exact approaches to compute them are impractical and only able to solve small instances. In this paper, we apply three local search-based metaheuristics for solving the problem. Results on 280 randomly generated instances with different sizes show the clear outperformance of the metaheuristic approaches over the exact method based on Mixed Integer Linear Programming.