Stable Population Games and Integrability for Evolutionary Dynamics∗

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. Furthermore, we prove that this set is globally asymptotically stable under a wide range of evolutionary dynamics. These convergence results for stable games are not as general as those for potential games: in addition to monotonicity of the dynamics, integrability of the agents’ revision protocols plays a key role.