# Entropic mean-field min-max problems via Best Response flow

arXiv: https://arxiv.org/abs/2306.03033 · HTML: https://mlsanity.com/paper/2306.03033/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2023.

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

- [A Fisher-Rao gradient flow for entropic mean-field min-max games](https://mlsanity.com/paper/2405.15834/) (2024)
- [Non-convex entropic mean-field optimization via Best Response flow](https://mlsanity.com/paper/2505.22760/) (2025)

## Abstract (arXiv)

We investigate the convergence properties of a continuous-time optimization method, the textitMean-Field Best Response flow, for solving convex-concave min-max games with entropy regularization. We introduce suitable Lyapunov functions to establish exponential convergence to the unique mixed Nash equilibrium. Additionally, we demonstrate the convergence of the fictitious play flow as a by-product of our analysis.