发表机构
The University of Hong Kong; Peking University（香港大学; 北京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种无超参数的简单确定性多项式时间算法，通过丰富Tsaknakis和Spirakis的优化框架，首次打破双矩阵博弈近似纳什均衡的1/3壁垒，实现约0.30954+δ的近似保证。
AI 中文摘要
双矩阵博弈中计算纳什均衡的PPAD完全性推动了针对$\epsilon$-近似纳什均衡的多项式时间算法的广泛研究。确定多项式时间内可达到的最强近似保证是近似纳什均衡复杂性中的一个基本问题。尽管持续努力，打破$1/3$壁垒长期以来一直被视为一个困难的开放问题。在本文中，我们通过提出一个简单、对称的确定性多项式时间算法给出了肯定回答，该算法没有可调超参数，并实现了约$0.30954+\delta$的近似保证。主要思想是用我们关于策略混合和自动化近似分析工作中的构建块来丰富Tsaknakis和Spirakis的优化框架，产生了一种新的算法结构，为改进的保证提供了概念性解释。
英文摘要
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.
