Evolutionary Algorithms for Computing Nash Equilibria in Dynamic Games

TL;DR

This paper introduces two evolutionary algorithms that effectively compute global Nash equilibria in complex dynamic games, overcoming limitations of classical methods in nonlinear and multi-player scenarios.

Contribution

It presents novel population-based evolutionary algorithms that directly search joint strategies without restrictive assumptions, improving global equilibrium approximation.

Findings

Algorithms successfully find more accurate Nash equilibria in complex dynamic games.

Methods outperform classical approaches in nonlinear and multi-player settings.

Approaches are less prone to local optima and applicable to general dynamic games.

Abstract

Dynamic nonzero sum games are widely used to model multi agent decision making in control, economics, and related fields. Classical methods for computing Nash equilibria, especially in linear quadratic settings, rely on strong structural assumptions and become impractical for nonlinear dynamics, many players, or long horizons, where multiple local equilibria may exist. We show through examples that such methods can fail to reach the true global Nash equilibrium even in relatively small games. To address this, we propose two population based evolutionary algorithms for general dynamic games with linear or nonlinear dynamics and arbitrary objective functions: a co evolutionary genetic algorithm and a hybrid genetic algorithm particle swarm optimization scheme. Both approaches search directly over joint strategy spaces without restrictive assumptions and are less prone to getting trapped in local Nash equilibria, providing more reliable approximations to global Nash solutions.