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arXiv · 2510.14907

Learnable Mixed Nash Equilibria are Collectively Rational

Geelon So·Yi-An Ma
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Abstract

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.

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Geelon So, Yi-An Ma. 2025-10-16. Learnable Mixed Nash Equilibria are Collectively Rational. https://arxiv.org/abs/2510.14907

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