Empirical Game-Theoretic Analysis in Mean Field Games

In this study, we demonstrate how empirical game-theoretical analysis (EGTA) can be applied to mean field games (MFGs). Since the utility function of a MFG is not generally linear in the distribution of the population, it is impractical to define an explicit payoff matrix for empirical game analysis as usual. Instead, we utilize query-based approaches without keeping an explicit payoff matrix. We propose an iterative EGTA framework to learn Nash equilibrium (NE) for MFGs and study the convergence of our algorithm from two aspects: the existence of NE in the empirical MFG and the convergence of iterative EGTA to NE of the full MFG. We test the performance of iterative EGTA in various games and show its superior performance against Fictitious Play under some common assumptions in EGTA. Finally, we discuss the limitations of applying iterative EGTA to MFGs as well as potential future research directions.