A Simple Algorithm Breaking the 1/3 Barrier for Approximate Nash Equilibria in Bimatrix Games
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, Dongchen, Li, Hanyu
Institutions: University of Hong Kong, Peking University
Language: English
Topic: Game Theory and Applications
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7220723432