Evolutionary stability with equilibrium entrants

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Abstract

The strategy that upsets a potential evolutionarily stable strategy may in itself be very unstable, or may differ from the candidate strategy only in irrelevant ways. This paper develops a solution concept addressing these difficulties. We lood for a set of Nash equilibria such that small groups of entrants whose members are satisfied with their entry cannot take the population out of the set. Such a set is robust to the iterated removal of weakly dominated strategies, depends only on the reduced normal form, and has the never a weak best response property. For generic two person extensive form games, such sets generate payoffs consistent with proper equilibria.

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I thank the Olin Foundation and the Sloan Foundation for financial support during the writing of this paper. I also thank the many people who made helpful comments on this work, including Abhijit Banerjee, Eric van Damme, Avinash Dixit, David Kreps, George Mailath, Akihiko Matsui, Paul Milgrom, Barry Nalebuff, Michele Piccione, Larry Samuelson, Christina Shannon, Joel Sobel, Jörgen Weibull, an anonymous referee, and participants in seminars at Princeton, Stanford, U.B.C., Wisconsin, the University of Pennsylvania, Northwestern, and Cornell.