Stable Games

We introduce a new class of population games called stable games. These games are characterized by self- defeating externalities: when agents revise their strategies, the improvements in the payoffs of strategies to which revising agents are switching are always exceeded by the improvements in the payoffs of strategies which revising agents are abandoning. Stable games subsume many well-known classes of examples, including zero-sum games, games with an interior ESS, wars of attrition, and concave potential games. We prove that the set of Nash equilibria of any stable game is convex. Finally, we show that the set of Nash equilibria of a stable game is globally asymptotically stable under various classes of evolutionary dynamics, classes that include the best response dynamic, the Brown-von Neumann-Nash dynamic, and the Smith dynamic.