Hofbauer, J.; Sandholm, W.; (2006) Stable games. (ELSE Working Papers 230). ESRC Centre for Economic Learning and Social Evolution: London, UK.

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Abstract

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.

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