# Learnable Mixed Nash Equilibria are Collectively Rational

arXiv: https://arxiv.org/abs/2510.14907 · HTML: https://mlsanity.com/paper/2510.14907/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 70 references that are in the map.
- First posted on arXiv 16 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [Cycles in adversarial regularized learning](https://mlsanity.com/paper/1709.02738/) (2017)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization](https://mlsanity.com/paper/1807.04252/) (2018)
- [No-regret learning and mixed Nash equilibria: They do not mix](https://mlsanity.com/paper/2010.09514/) (2020)
- [Differentiable Game Mechanics](https://mlsanity.com/paper/1905.04926/) (2019)
- [On Last-Iterate Convergence Beyond Zero-Sum Games](https://mlsanity.com/paper/2203.12056/) (2022)
- [Survival of the strictest: Stable and unstable equilibria under regularized learning with partial information](https://mlsanity.com/paper/2101.04667/) (2021)
- [Nash Convergence of Gradient Dynamics in Iterated General-Sum Games](https://mlsanity.com/paper/1301.3892/) (2013)
- [Lyapunov Theory for Discrete Time Systems](https://mlsanity.com/paper/1809.05289/) (2018)
- [Payoff Performance of Fictitious Play](https://mlsanity.com/paper/1308.4049/) (2013)
- [Stochastic Multiplicative Weights Updates in Zero-Sum Games](https://mlsanity.com/paper/2110.02134/) (2021)
- [Fast Convergence of Optimistic Gradient Ascent in Network Zero-Sum Extensive Form Games](https://mlsanity.com/paper/2207.08426/) (2022)
- [Optimistic Gradient Descent Ascent in Zero-Sum and General-Sum Bilinear Games](https://mlsanity.com/paper/2208.03085/) (2022)

## Abstract (arXiv)

We extend the study of learning in games to dynamics that exhibit non-asymptotic stability. We do so through the notion of uniform stability, which is concerned with equilibria of individually utility-seeking dynamics. Perhaps surprisingly, it turns out to be closely connected to economic properties of collective rationality. Up to strategic equivalence, if a mixed equilibrium is uniformly stable, then it is weakly Pareto optimal; there is no way for all players to improve by jointly deviating from the equilibrium. This is a form of collective rationality that rules out the types of behaviors in the prisoner's dilemma or the tragedy of the commons. Moreover, we show that uniform stability determines the last-iterate convergence behavior for the family of incremental smoothed best-response dynamics, used to model individual and corporate behaviors in the markets. Unlike dynamics around strict equilibria, which can stabilize to socially-inefficient solutions, individually utility-seeking behaviors near mixed Nash equilibria lead to collective rationality.