# Optimal Coarse Correlated Equilibria in Mean Field Games: Linear Programming and No-Regret Learning

arXiv: https://arxiv.org/abs/2606.20062 · HTML: https://mlsanity.com/paper/2606.20062/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 73 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 8 of 8)

- [Learning Equilibria in Mean-Field Games: Introducing Mean-Field PSRO](https://mlsanity.com/paper/2111.08350/) (2021)
- [Learning in anonymous nonatomic games with applications to first-order mean field games](https://mlsanity.com/paper/1704.00378/) (2017)
- [Learning Correlated Equilibria in Mean-Field Games](https://mlsanity.com/paper/2208.10138/) (2022)
- [Proximal Regret and Proximal Correlated Equilibria: A New Tractable Solution Concept for Online Learning and Games](https://mlsanity.com/paper/2511.01852/) (2025)
- [Mirror Descent-Ascent for mean-field min-max problems](https://mlsanity.com/paper/2402.08106/) (2024)
- [Deep Incentive Design with Differentiable Equilibrium Blocks](https://mlsanity.com/paper/2603.07705/) (2026)
- [Continuous-time mean field games: a primal-dual characterization](https://mlsanity.com/paper/2503.01042/) (2025)
- [On Information Controls](https://mlsanity.com/paper/2602.07318/) (2026)

## Abstract (arXiv)

We introduce optimal coarse correlated equilibria for continuous-time mean field games. A coarse correlated equilibrium is a randomized recommendation scheme from which no player can gain by ignoring the recommendation and switching to an alternative strategy. The problem is as follows: a moderator selects, among all mean-field coarse correlated equilibria, one that optimizes a prescribed performance criterion, which may differ from the representative player's objective. After formulating the problem, we develop a linear programming (LP) formulation, prove the existence of optimal LP coarse correlated equilibria, and relate the LP characterization to the original probabilistic setting. Building on this characterization, we design a no-regret primal-dual algorithm, based on an equivalent Lagrangian formulation of the external-regret constraint, for learning such equilibria. We provide explicit convergence rates for the learning algorithm, and numerical examples illustrate the method.