这篇论文用严格实验告诉你：不同博弈算法选出的纳什均衡不一样，R-NaD倾向最大熵，CFR+倾向低熵，这会影响你对付弱对手的鲁棒性。
这篇论文研究双人零和博弈中纳什均衡的算法依赖性选择。在六个可精确求解的博弈（包括二维纳什多面体和Kuhn扑克）中，R-NaD和磁镜下降等正则化最后迭代方法总是选择最大熵成员（在二维多面体上精确，在Kuhn中达到99.7%最大熵）。而CFR、CFR+和虚拟博弈等遗憾平均方法则漂移到低熵面。在180个随机博弈的实验中，R-NaD在100%收敛的博弈中达到最大熵，而CFR+在94%的博弈中严格低于该值（配对Wilcoxon p<10^-27）。论文还报告了两个否定结果：去除CFR的投影未消除边界漂移；R-NaD的选择依赖初始锚点。
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 information projection of their uniform reference onto the Nash set -- exactly on the 2-D polytope and at 99.7% of maximum entropy in Kuhn -- while regret-averaging methods (CFR, CFR+, fictitious play) drift to a lower-entropy face; we confirm this on a randomized 180-game ensemble, where R-NaD attains the maximum-entropy member in 100% of converged games while CFR+ sits strictly below it in 94% (paired Wilcoxon p < 10^-27); (iii) the selected member has downstream consequences against sub-optimal opponents that scale with sequential/hidden-information structure but stay bounded -- in Kuhn the max-entropy member is a strictly better hedge, whereas on the matrix games the members differ without either dominating. We also report two negative results correcting common intuitions: removing CFR's positive-orthant (max(R,0)) projection does not eliminate boundary drift; and R-NaD's selection is anchor-following, not initialization-independent. We state the maximum-entropy / I-projection characterization as a strongly data-supported conjecture, checked throughout against analytic ground truth.