[论文] [论文] Which Nash Equilibrium? Solver-Dependent Selection on Zero-Sum Na...

论文概要

研究领域: ML 作者: Luis Leal 发布时间: 2026-06-26 arXiv: 2606.28308

中文摘要

许多双人零和博弈没有唯一的纳什均衡，而是存在一组凸均衡集。标准求解器各自收敛到某个均衡，并被当作可互换的。我们问它们是否反而选择纳什集合的不同成员，作为算法而非种子的系统函数。使用六个博弈的表格精确可解测试平台，我们发现（i）选择由算法决定，而非种子；（ii）正则化最后迭代方法（R-NaD、磁镜下降）选择最大熵成员，而后悔平均方法（CFR、CFR+、虚构博弈）漂移到较低熵面；我们在随机180博弈集合上确认这一点；（iii）所选成员对次优对手有下游后果。我们还报告两个纠正常见直觉的负面结果：移除CFR的正交象限投影并不能消除边界漂移；R-NaD的选择是锚跟随的，而非初始化独立的。

原文摘要

Many two-player zero-sum games admit not a unique Nash equilibrium but a convex set of them: a polytope of profiles that all share the minimax value V* yet prescribe different behaviour. Standard solvers each converge to some equilibrium and are treated as interchangeable. We ask whether they instead select different members of the Nash set, systematically as a function of the algorithm rather than the seed. Using a tabular, exactly solvable testbed of six games with analytically known Nash sets -- including a two-dimensional Nash polytope and Kuhn poker -- we find that (i) selection is determined by the algorithm, not the seed, but families differ only on asymmetric Nash sets; (ii) regularized last-iterate methods (R-NaD, magnetic mirror descent) select the maximum-entropy member, the inf...

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