Static stability in economic models means negative incentives for deviation from equilibrium strategies, which we expect to assure a return to equilibrium, i.e., dynamic stability, as long as agents respond to incentives. There have been many attempts to prove this link, especially in evolutionary game theory, yielding both negative and positive results. This paper presents a universal and intuitive approach to this link. We prove that static stability assures dynamic stability if agents' choices of switching strategies are rationalizable by introducing costs and constraints in those switching decisions. This idea guides us to define \textit{net }gains from switches as the payoff improvement after deducting the costs. Under rationalizable dynamics, an agent maximizes the expected net gain subject to the constraints. We prove that the aggregate maximized expected net gain works as a Lyapunov function. It also explains reasons behind the known negative results. While our analysis here is confined to myopic evolutionary dynamics in population games, our approach is applicable to more complex situations.

翻译：经济模型中的静态稳定性意味着偏离均衡策略会产生负激励，只要主体对激励做出反应，我们预期这能确保回归均衡，即动态稳定性。已有许多尝试证明这种联系，尤其是在演化博弈论中，但既有负面结果也有正面结果。本文提出了一种通用且直观的方法来建立这种联系。我们证明，如果在策略转换决策中引入成本和约束，使得主体的转换策略选择具有可理性化特征，那么静态稳定性就能保证动态稳定性。这一思路引导我们将转换的净增益定义为扣除成本后的收益改进。在可理性化动力学下，主体在约束条件下最大化期望净增益。我们证明，加总后的最大化期望净增益可作为李雅普诺夫函数。这同时也解释了已知负面结果背后的原因。尽管本文的分析仅限于群体博弈中的近视演化动力学，但我们的方法适用于更复杂的情形。