Learning in Discounted-cost and Average-cost Mean-field Games. (arXiv:1912.13309v3 [eess.SY] UPDATED)

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 …

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