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

arXiv: https://arxiv.org/abs/1912.13309 · HTML: https://mlsanity.com/paper/1912.13309/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2019.

## Built on by (most cited first, 1 of 1)

- [Learning Regularized Graphon Mean-Field Games with Unknown Graphons](https://mlsanity.com/paper/2310.17531/) (2023)

## Abstract (arXiv)

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.