标题： 逆时针耗散性、势博弈与进化纳什均衡学习 显示英文标题

标题： Counterclockwise Dissipativity, Potential Games and Evolutionary Nash Equilibrium Learning

摘要： 我们使用系统理论的无源性方法来研究大规模参与战略非合作互动的代理群体中的进化纳什均衡学习。 代理遵循学习规则（简称规则）来体现其战略偏好，收益机制为可用策略分配收益。 群体的整体战略配置是相关进化动力系统的状态。 进化纳什均衡学习指的是该状态收敛到收益机制的纳什均衡集。 大多数方法考虑无记忆收益机制，例如势博弈。 最近，使用$\delta$-无源性和平衡独立无源性（EIP）的方法引入了动态收益机制。 然而，当代理遵循表现出“模仿”行为的规则时，如复制者动力学中那样，$\delta$-无源性不成立。 相反，EIP适用于复制者动力学，但不适用于$\delta$-无源规则。 我们使用逆时针耗散性（CCW）来填补这一空白。 首先，我们证明连续无记忆收益机制是 CCW 的当且仅当它们是势博弈。 随后，在（可能动态的）CCW 收益机制下，我们为由模仿规则和连续$\delta$-无源规则张成的凸锥内的任何规则建立进化纳什均衡学习。 显示英文摘要

摘要： We use system-theoretic passivity methods to study evolutionary Nash equilibria learning in large populations of agents engaged in strategic, non-cooperative interactions. The agents follow learning rules (rules for short) that capture their strategic preferences and a payoff mechanism ascribes payoffs to the available strategies. The population's aggregate strategic profile is the state of an associated evolutionary dynamical system. Evolutionary Nash equilibrium learning refers to the convergence of this state to the Nash equilibria set of the payoff mechanism. Most approaches consider memoryless payoff mechanisms, such as potential games. Recently, methods using $\delta$-passivity and equilibrium independent passivity (EIP) have introduced dynamic payoff mechanisms. However, $\delta$-passivity does not hold when agents follow rules exhibiting ``imitation" behavior, such as in replicator dynamics. Conversely, EIP applies to the replicator dynamics but not to $\delta$-passive rules. We address this gap using counterclockwise dissipativity (CCW). First, we prove that continuous memoryless payoff mechanisms are CCW if and only if they are potential games. Subsequently, under (possibly dynamic) CCW payoff mechanisms, we establish evolutionary Nash equilibrium learning for any rule within a convex cone spanned by imitation rules and continuous $\delta$-passive rules.