# Mean Field Games with Ergodic cost for Discrete Time Markov Processes

arXiv: https://arxiv.org/abs/1510.08968 · HTML: https://mlsanity.com/paper/1510.08968/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2015.

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

- [Stationary Robust Mean-Field Games under Model Mismatches](https://mlsanity.com/paper/2606.22579/) (2026)
- [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)

We consider mean field games with ergodic cost in the framework of a general discrete time controlled Markov processes. The state space of the processes is given by a general σ-compact Polish space. Under certain conditions, we show the existence of a mean field game equilibrium. We also study the N-person game where the players interacts with each other via their empirical measure. We show that the N-person game has Nash equilibrium and as N tends to infinity the equilibria converge to a mean field game solution.