Learning Pure-Strategy Nash Equilibria in Networked Multi-Agent Systems with Uncertainty

A multi-agent system with uncertainty entails a set of agents intent on maximizing their local utility functions that depend on the actions of other agents and a state of the world while having partial and different information about actions of other agents and the state of the world. When agents repeatedly have to make decisions in these settings, we propose a general class of decision-making dynamics based on the Fictitious Play (FP) algorithm with inertia. We show convergence of the proposed algorithm to pure Nash equilibria for the class of weakly acyclic games-a structural assumption on local utility functions that guarantees existence of pure Nash equilibria-as long as the predictions of the agents of their local utilities satisfy a mild asymptotic accuracy condition. Using the results on the general dynamics, the paper proposes distributed implementations of the FP algorithm with inertia suited for networked multi-agent systems and shows its convergence to pure Nash equilibria. Numerical examples corroborate the analysis providing insights to convergence time.