# Discrete-time average-cost mean-field games on Polish spaces

arXiv: https://arxiv.org/abs/1908.08793 · HTML: https://mlsanity.com/paper/1908.08793/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2019.

## Built on by (most cited first, 2 of 2)

- [Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games](https://mlsanity.com/paper/2505.22781/) (2025)
- [Entropy-Regularized Mean-Field Games with Average-Reward Criterion: Span-Seminorm Contractions and Model-Free Learning](https://mlsanity.com/paper/2610.15871/) (2026)

## Abstract (arXiv)

In stochastic dynamic games, when the number of players is sufficiently large and the interactions between agents depend on empirical state distribution, one way to approximate the original game is to introduce infinite-population limit of the problem. In the infinite population limit, a generic agent is faced with a so-called mean-field game. In this paper, we study discrete-time mean-field games with average-cost criteria. Using average cost optimality equation and Kakutani's fixed point theorem, we establish the existence of Nash equilibria for mean-field games under drift and minorization conditions on the dynamics of each agent. Then, we show that the equilibrium policy in the mean-field game, when adopted by each agent, is an approximate Nash equilibrium for the corresponding finite-agent game with sufficiently many agents.