Learning in Discounted-cost and Average-cost Mean-field Games
This work addresses computational challenges in multi-agent systems with many agents, offering a method for equilibrium approximation in mean-field games, though it appears incremental as it builds on existing mean-field game theory with specific cost structures.
The paper tackles the problem of learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic dynamics under both average and discounted costs by introducing a contraction-based mean-field equilibrium operator and a learning algorithm that approximates it, establishing error bounds and showing the learned equilibrium provides approximate Nash equilibria for finite-agent games.
We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear stochastic state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator, whose fixed point is a mean-field equilibrium (i.e. equilibrium in the infinite population limit). We first prove that this operator is a contraction, and propose a learning algorithm to compute an approximate mean-field equilibrium by approximating the MFE operator with a random one. Moreover, using the contraction property of the MFE operator, we establish the error analysis of the proposed learning algorithm. We then show that the learned mean-field equilibrium constitutes an approximate Nash equilibrium for finite-agent games.