We investigate the stability of mixed strategy equilibria in 2 person (bimatrix) games under perturbed best response dynamics. A mixed equilibrium is asymptotically stable under all such dynamics if and only if the game is linearly equivalent to a zero sum game. In this case, the mixed equilibrium is also globally asymptotically stable. Global convergence to the set of perturbed equilibria is shown also for (rescaled) partnership games, also known as potential games. Lastly, mixed equilibria of partnership games are shown (...) to be always unstable under all dynamics of this class. (shrink)

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 players are switching are always exceeded by the improvements in the payoffs of strategies which revising players are abandoning. We show that 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, and offer an elementary proof of existence of equilibrium. Finally, we show that the set of Nash equilibria of a stable game is globally asymptotically stable under a variety of evolutionary dynamics. These convergence results are proved by constructing Lyapunov functions defined in terms of revision potentials—that is, potential functions for the protocols agents follow when they consider switching strategies. (shrink)