# Approximate Nash Equilibria in Partially Observed Stochastic Games with Mean-Field Interactions

arXiv: https://arxiv.org/abs/1705.02036 · HTML: https://mlsanity.com/paper/1705.02036/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2017.

## Built on by (most cited first, 8 of 8)

- [Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning](https://mlsanity.com/paper/2102.01585/) (2021)
- [Learning Graphon Mean Field Games and Approximate Nash Equilibria](https://mlsanity.com/paper/2112.01280/) (2021)
- [A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.03859/) (2022)
- [Unified continuous-time q-learning for mean-field game and mean-field control problems](https://mlsanity.com/paper/2407.04521/) (2024)
- [Discrete-Time Mean Field Control with Environment States](https://mlsanity.com/paper/2104.14900/) (2021)
- [On Diffusion Models for Multi-Agent Partial Observability: Shared Attractors, Error Bounds, and Composite Flow](https://mlsanity.com/paper/2410.13953/) (2024)
- [Recurrent Structural Policy Gradient for Partially Observable Mean Field Games](https://mlsanity.com/paper/2602.20141/) (2026)
- [Stationary Robust Mean-Field Games under Model Mismatches](https://mlsanity.com/paper/2606.22579/) (2026)

## Abstract (arXiv)

Establishing the existence of Nash equilibria for partially observed stochastic dynamic games is known to be quite challenging, with the difficulties stemming from the noisy nature of the measurements available to individual players (agents) and the decentralized nature of this information. When the number of players is sufficiently large and the interactions among agents is of the mean-field type, one way to overcome this challenge is to investigate the infinite-population limit of the problem, which leads to a mean-field game. In this paper, we consider discrete-time partially observed mean-field games with infinite-horizon discounted cost criteria. Using the technique of converting the original partially observed stochastic control problem to a fully observed one on the belief space and the dynamic programming principle, we establish the existence of Nash equilibria for these game models under very mild technical conditions. Then, we show that the mean-field equilibrium policy, when adopted by each agent, forms an approximate Nash equilibrium for games with sufficiently many agents.