Learning Mean-Field Games with Discounted and Average Costs
Berkay Anahtarci, Can Deha Kariksiz, Naci Saldi; 24(17):1−59, 2023.
Abstract
This study focuses on learning approximate Nash equilibria for discrete-time mean-field games with stochastic nonlinear state dynamics subject to both average and discounted costs. The authors introduce a mean-field equilibrium (MFE) operator, which represents a fixed point that corresponds to a mean-field equilibrium, i.e., an equilibrium in the infinite population limit. The study proves that this operator is a contraction and proposes a learning algorithm to compute an approximate mean-field equilibrium by approximating the MFE operator with a random one. Additionally, the authors establish the error analysis of the proposed learning algorithm by utilizing the contraction property of the MFE operator. Furthermore, they demonstrate that the learned mean-field equilibrium constitutes an approximate Nash equilibrium for finite-agent games.
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