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Static stability in economic models means negative incentives for deviationfrom equilibrium strategies, which we expect to assure a return to equilibrium,i.e., dynamic stability, as long as agents respond to incentives. There havebeen many attempts to prove this link, especially in evolutionary game theory,yielding both negative and positive results. This paper presents a universaland intuitive approach to this link. We prove that static stability assuresdynamic stability if agents' choices of switching strategies are rationalizableby introducing costs and constraints in those switching decisions. This ideaguides us to define \textit{net }gains from switches as the payoff improvementafter deducting the costs. Under rationalizable dynamics, an agent maximizesthe expected net gain subject to the constraints. We prove that the aggregatemaximized expected net gain works as a Lyapunov function. It also explainsreasons behind the known negative results. While our analysis here is confinedto myopic evolutionary dynamics in population games, our approach is applicableto more complex situations.

Net gains in evolutionary dynamics: A unifying and intuitive approach to dynamic stability