We investigate how the framework of mean-field games may be used to investigate strategic interactions in large heterogeneous populations with interactions which are not necessarily symmetric. We consider strategic interactions in a population of players which may be partitioned into near-homogeneous sub-populations subject to peer group effects and interactions across groups. We prove a quantitative homogenization result for multi-player games in this setting: we show that  ϵ-Nash equilibria of a general multi-player game with heterogeneity may be computed in terms of the Nash equilibria of an auxiliary multi-population mean-field game. We provide explicit non-asymptotic bounds for the distance from optimality in terms of the number of players and the deviations from homogeneity in sub-populations. We show that the best mean-field approximation corresponds to an optimal partition which may be obtained as the solution of a mixed-integer program.

We illustrate the results for a multipopulation epidemic model and a multi-agent reinforcement learning framework for a population of Linear-Quadratic controllers.