混合纳什均衡若稳定，则集体理性，避免囚徒困境。
Learnable Mixed Nash Equilibria are Collectively Rational
- 用一致稳定性分析非渐近稳定的博弈动态
- 均匀稳定混合均衡必弱帕累托最优
- 适合研究市场行为与集体理性的学者
我们拓展了博弈学习的研究，关注非渐近稳定的动态。通过一致稳定性概念，该概念聚焦个体逐利行为的均衡。令人惊讶的是，它与集体理性经济性质密切相关：在策略等价意义下，若一个混合均衡是均匀稳定的，则它是弱帕累托最优的——不存在所有参与者联合偏离均衡而全都能获益的情况。这排除了囚徒困境或公地悲剧类行为。此外，我们证明一致稳定性决定了增量平滑最佳响应动态族的最终迭代收敛行为，该类动态用于建模市场中的个体与企业行为。与严格均衡附近可能出现社会效率低下的结果不同，个体逐利行为在混合纳什均衡附近会导向集体理性。
原文摘要 · Abstract (English)
We extend the study of learning in games to dynamics that exhibit non-asymptotic stability. We do so through the notion of uniform stability, which is concerned with equilibria of individually utility-seeking dynamics. Perhaps surprisingly, it turns out to be closely connected to economic properties of collective rationality. Up to strategic equivalence, if a mixed equilibrium is uniformly stable, then it is weakly Pareto optimal; there is no way for all players to improve by jointly deviating from the equilibrium. This is a form of collective rationality that rules out the types of behaviors in the prisoner's dilemma or the tragedy of the commons. Moreover, we show that uniform stability determines the last-iterate convergence behavior for the family of incremental smoothed best-response dynamics, used to model individual and corporate behaviors in the markets. Unlike dynamics around strict equilibria, which can stabilize to socially-inefficient solutions, individually utility-seeking behaviors near mixed Nash equilibria lead to collective rationality.
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