  We present a simulation-based approach for solution of mean field games
(MFGs), using the framework of empirical game-theoretical analysis (EGTA). Our
primary 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. We present Fictitious Play (FP) and Replicator
Dynamics as two subroutines for computing the empirical game equilibrium. Each
subroutine is implemented with a query-based method rather than maintaining an
explicit payoff matrix as in typical EGTA methods due to a representation issue
we highlight for MFGs. By introducing game model learning and regularization,
we significantly improve the sample efficiency of the primary method without
sacrificing the overall learning performance. Theoretically, we prove that a
Nash equilibrium (NE) exists in the empirical MFG and show the convergence of
iterative EGTA to NE of the full MFG with either subroutine. We test the
performance of iterative EGTA in various games and show that it outperforms
directly applying FP to MFGs in terms of iterations of strategy introduction.
