Before revision: This paper presents a universal and economically intuitive approach to linking static and dynamic stability. In economics, static stability is traditionally defined by negative relationship between endogenous and exogenous variables in a model: for a population game , this is characterized by negative semidefiniteness of the Jacobian matrix of the payoff function. We consider economically reasonable dynamics, in which we can justify agents' choices of new strategies as optimal choices possibly by introducing additional costs and constraints .
After revision: Static stability in an economic model typically 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 offers a universal and intuitive approach to this link. We prove static stability assures dynamic stability as long as agents' decisions of switching strategies are rationalizable by revealing costs and constraints .