Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning
This work provides a method for solving a class of Mean Field Games that were previously intractable due to non-contractive fixed point operators, which is significant for researchers and practitioners working with many-agent systems in game theory and reinforcement learning.
This paper addresses the challenge of solving discrete-time finite Mean Field Games (MFGs) where the fixed point operators are non-contractive, which prevents convergence using standard fixed point iteration. By incorporating entropy-regularization and Boltzmann policies, the authors achieve provable convergence to approximate fixed points, thereby reaching approximate Nash equilibria.
The recent mean field game (MFG) formalism facilitates otherwise intractable computation of approximate Nash equilibria in many-agent settings. In this paper, we consider discrete-time finite MFGs subject to finite-horizon objectives. We show that all discrete-time finite MFGs with non-constant fixed point operators fail to be contractive as typically assumed in existing MFG literature, barring convergence via fixed point iteration. Instead, we incorporate entropy-regularization and Boltzmann policies into the fixed point iteration. As a result, we obtain provable convergence to approximate fixed points where existing methods fail, and reach the original goal of approximate Nash equilibria. All proposed methods are evaluated with respect to their exploitability, on both instructive examples with tractable exact solutions and high-dimensional problems where exact methods become intractable. In high-dimensional scenarios, we apply established deep reinforcement learning methods and empirically combine fictitious play with our approximations.