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arXiv · 2610.05317

A Simple Algorithm Breaking the 1/3 Barrier for Approximate Nash Equilibria in Bimatrix Games

Dongchen Li·Hanyu Li
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Abstract

The PPAD-completeness of computing Nash equilibria in bimatrix games has driven extensive research into polynomial-time algorithms for $ε$-approximate Nash equilibria. Determining the strongest approximation guarantee achievable in polynomial time is a fundamental question in the complexity of approximate Nash equilibria. Despite sustained efforts, breaking the $1/3$ barrier has long been regarded as a difficult open problem. In this paper, we give an affirmative answer by proposing a simple, symmetric deterministic polynomial-time algorithm that has no tunable hyperparameters and achieves an approximation guarantee of approximately $0.30954+δ$. The main idea is to enrich the optimization framework of Tsaknakis and Spirakis with building blocks drawn from our work on strategy mixing and automated approximation analysis, yielding a new algorithmic structure that provides a conceptual explanation for the improved guarantee.

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Dongchen Li, Hanyu Li. 2026-10-04. A Simple Algorithm Breaking the 1/3 Barrier for Approximate Nash Equilibria in Bimatrix Games. https://arxiv.org/abs/2610.05317

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