Learning in Discounted-cost and Average-cost Mean-field Games

• URL: http://arxiv.org/abs/1912.13309v3
• Date: Thu, 10 Nov 2022 18:44:59 GMT
• Title: Learning in Discounted-cost and Average-cost Mean-field Games
• Authors: Berkay Anahtarc{\i}, Can Deha Kar{\i}ks{\i}z, and Naci Saldi
• Abstract summary: We consider learning approximate Nash equilibria for discrete-time mean-field games with nonlinear state dynamics. We first prove that this operator is a contraction, and propose a learning algorithm to compute an approximate mean-field equilibrium. We then show that the learned mean-field equilibrium constitutes an approximate Nash equilibrium for finite-agent games.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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