# Learning Correlated Equilibria in Mean-Field Games

arXiv: https://arxiv.org/abs/2208.10138 · HTML: https://mlsanity.com/paper/2208.10138/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 90 references that are in the map.
- First posted on arXiv 22 Aug 2022.

## Builds on (most cited first, 30 of 37)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning](https://mlsanity.com/paper/1711.00832/) (2017)
- [DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker](https://mlsanity.com/paper/1701.01724/) (2017)
- [OpenSpiel: A Framework for Reinforcement Learning in Games](https://mlsanity.com/paper/1908.09453/) (2019)
- [Solving Large Imperfect Information Games Using CFR+](https://mlsanity.com/paper/1407.5042/) (2014)
- [Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications](https://mlsanity.com/paper/2007.03458/) (2020)
- [Concave Utility Reinforcement Learning: the Mean-Field Game Viewpoint](https://mlsanity.com/paper/2106.03787/) (2021)
- [α-Rank: Multi-Agent Evaluation by Evolution](https://mlsanity.com/paper/1903.01373/) (2019)
- [Q-Learning in Regularized Mean-field Games](https://mlsanity.com/paper/2003.12151/) (2020)
- [Learning in Mean Field Games: the Fictitious Play](https://mlsanity.com/paper/1507.06280/) (2015)
- [Scaling up Mean Field Games with Online Mirror Descent](https://mlsanity.com/paper/2103.00623/) (2021)
- [A General Framework for Learning Mean-Field Games](https://mlsanity.com/paper/2003.06069/) (2020)
- [Mean Field Games and Applications: Numerical Aspects](https://mlsanity.com/paper/2003.04444/) (2020)
- [Hindsight and Sequential Rationality of Correlated Play](https://mlsanity.com/paper/2012.05874/) (2020)
- [Multi-Agent Training beyond Zero-Sum with Correlated Equilibrium Meta-Solvers](https://mlsanity.com/paper/2106.09435/) (2021)
- [Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance](https://mlsanity.com/paper/2107.04568/) (2021)
- [No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium](https://mlsanity.com/paper/2004.00603/) (2020)
- [Online Learning in Markov Decision Processes with Adversarially Chosen Transition Probability Distributions](https://mlsanity.com/paper/1303.3055/) (2013)
- [Coarse Correlation in Extensive-Form Games](https://mlsanity.com/paper/1908.09893/) (2019)
- [Efficient Deviation Types and Learning for Hindsight Rationality in Extensive-Form Games](https://mlsanity.com/paper/2102.06973/) (2021)
- [Reinforcement Learning for Mean Field Games, with Applications to Economics](https://mlsanity.com/paper/2106.13755/) (2021)
- [Learning Equilibria in Mean-Field Games: Introducing Mean-Field PSRO](https://mlsanity.com/paper/2111.08350/) (2021)
- [Mean-Field-Type Games in Engineering](https://mlsanity.com/paper/1605.03281/) (2016)
- [Optimal incentives to mitigate epidemics: a Stackelberg mean field game approach](https://mlsanity.com/paper/2011.03105/) (2020)
- [Correlated equilibria and mean field games: a simple model](https://mlsanity.com/paper/2004.06185/) (2020)
- [Payoff Performance of Fictitious Play](https://mlsanity.com/paper/1308.4049/) (2013)
- [Empirical Game-Theoretic Analysis for Mean Field Games](https://mlsanity.com/paper/2112.00900/) (2021)
- [Notions of Anonymity, Fairness and Symmetry for Finite Strategic-Form Games](https://mlsanity.com/paper/1311.4766/) (2013)
- [Mean field games via controlled martingale problems: Existence of Markovian equilibria](https://mlsanity.com/paper/1404.2642/) (2014)
- [On the (in)efficiency of MFG equilibria](https://mlsanity.com/paper/1802.06637/) (2018)

## Built on by (most cited first, 6 of 6)

- [MF-OML: Online Mean-Field Reinforcement Learning with Occupation Measures for Large Population Games](https://mlsanity.com/paper/2405.00282/) (2024)
- [Scalable Task-Driven Robotic Swarm Control via Collision Avoidance and Learning Mean-Field Control](https://mlsanity.com/paper/2209.07420/) (2022)
- [Bounded Rationality Equilibrium Learning in Mean Field Games](https://mlsanity.com/paper/2411.07099/) (2024)
- [The Learning Approach to Games](https://mlsanity.com/paper/2503.00227/) (2025)
- [Vulnerable Agent Identification in Large-Scale Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2509.15103/) (2025)
- [Optimal Coarse Correlated Equilibria in Mean Field Games: Linear Programming and No-Regret Learning](https://mlsanity.com/paper/2606.20062/) (2026)

## Abstract (arXiv)

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an N-player game typically grows exponentially with N, standard game theoretic analysis becomes effectively infeasible beyond a low number of players. Recent approaches have gone around this limitation by instead considering Mean-Field games, an approximation of anonymous N-player games, where the number of players is infinite and the population's state distribution, instead of every individual player's state, is the object of interest. The practical computability of Mean-Field Nash equilibria, the most studied Mean-Field equilibrium to date, however, typically depends on beneficial non-generic structural properties such as monotonicity or contraction properties, which are required for known algorithms to converge. In this work, we provide an alternative route for studying Mean-Field games, by developing the concepts of Mean-Field correlated and coarse-correlated equilibria. We show that they can be efficiently learnt in all games, without requiring any additional assumption on the structure of the game, using three classical algorithms. Furthermore, we establish correspondences between our notions and those already present in the literature, derive optimality bounds for the Mean-Field - N-player transition, and empirically demonstrate the convergence of these algorithms on simple games.