Empirical Game-Theoretic Analysis in Mean Field Games

We present a simulation-based approach for solution of mean field games (MFGs), using the framework of empirical game-theoretical analysis (EGTA). Our method employs a version of the double oracle, iteratively adding strategies based on best response to the equilibrium of the empirical MFG among strategies considered so far. The empirical game equilibrium is computed with a query-based method, rather than maintaining an explicit payoff matrix as in typical EGTA methods. We show that NE exist in the empirical MFG and study the convergence of iterative EGTA to NE of the full MFG. We test the performance of iterative EGTA in various games and show that it outperforms in terms of iterations of strategy introduction. Finally, we discuss the limitations of applying iterative EGTA to MFGs as well as potential future research directions.