A Bayesian Optimization Approach to Compute Nash Equilibrium of Potential Games Using Bandit Feedback

Abstract

Abstract Computing a Nash equilibrium for strategic multi-agent systems is challenging for black box systems. Motivated by the ubiquity of games involving exploitation of common resources, this paper considers the above problem for potential games. We use a Bayesian optimization framework to obtain novel algorithms to solve finite (discrete action spaces) and infinite (real interval action spaces) potential games, utilizing the structure of potential games. Numerical results illustrate the efficiency of the approach in computing a Nash equilibrium of static potential games and linear Nash equilibrium of dynamic potential games.