Before revision:  In economics, static stability is traditionally defined as a notion about how incentives respond to choices : for a population game, it means that, on average, the payoff of a strategy responds negatively to an increase in the share of the strategy. This is characterized by negative definiteness of the Jacobian matrix of the payoff function and satisfied globally in a contractive game and locally at a regular ESS.
After revision:  In economics, static stability is traditionally defined as a notion about how incentives respond to choices : for a population game, this is characterized by negative definiteness of the Jacobian matrix of the payoff function and satisfied globally in a contractive game and locally at a regular ESS.