发表机构
University of Maryland（马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对大规模种群动态收益机制下的演化纳什均衡学习，利用逆时针耗散性框架，通过Bregman散度构造与规则无关的Lyapunov函数，建立全局渐近稳定性，并以拥堵博弈验证。
AI 中文摘要
我们研究在大规模种群中，当收益由动态机制生成时的演化纳什均衡学习问题。逆时针耗散性（CCW）提供了一个类似无源性的框架，用于在满足自然收益对齐条件的所谓良态学习规则的广泛凸锥下建立学习/收敛性；该条件要求，在远离均衡时，种群的状态（策略分布）沿着与收益正相关的方向移动。该凸锥在锥组合下封闭，并涵盖广泛的免噪声规则，包括不连续规则（如最优响应）、模仿规则（如并非 δ-无源性的复制者规则），以及所有免噪声的 δ-无源性规则。现有的 CCW 结果不需要了解特定规则，但仅建立收敛性，而未提供 Lyapunov 函数或 Lyapunov 稳定性。我们开发了一种方法论来弥合这一差距，通过从收益机制的 CCW 存储函数构造与规则无关的 Lyapunov 函数。对于一类非线性的预期机制（其中智能体将当前收益与平滑化种群状态相关的收益进行比较），我们证明了存储函数可以导出为 Bregman 散度。由此产生的 Lyapunov 函数将势能缺口与该散度相结合，并建立全局渐近稳定性。一个具有非线性拥堵增长收费的拥堵博弈实例说明了这些结果。
英文摘要
We study evolutionary Nash equilibrium learning in large populations whose payoffs are generated by dynamic mechanisms. Counterclockwise dissipativity (CCW) provides a passivity-like framework for establishing learning/convergence under a broad convex cone of so-called well-behaved learning rules satisfying a natural payoff-alignment condition according to which, away from equilibria, the population's state (strategic profile) moves in a direction positively correlated with the payoffs. The cone is closed under conic combinations and encompasses a broad range of noise-free rules, including discontinuous rules such as best response, imitative rules such as the replicator rule that is not $δ$-passive, and all noise-free $δ$-passive rules. Existing CCW results require no knowledge of the particular rule, but establish convergence without providing a Lyapunov function or Lyapunov stability. We develop a methodology that closes this gap by constructing rule-independent Lyapunov functions from CCW storage functions of the payoff mechanism. For a nonlinear class of anticipatory mechanisms, in which agents compare current payoffs with those associated with a smoothed population state, we show that a storage can be derived as a Bregman divergence. The resulting Lyapunov function combines a potential gap with this divergence and establishes global asymptotic stability. A congestion game with a nonlinear congestion-growth toll illustrates the results.
