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The B.E. Journal of Theoretical Economics

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Stochastic Stability in Finitely Repeated Two Player Games

Jack Robles1

1Victoria University of Wellington,

Citation Information: The B.E. Journal of Theoretical Economics. Volume 11, Issue 1, ISSN (Online) 1935-1704, DOI: 10.2202/1935-1704.1686, April 2011

Publication History

Published Online:
2011-04-27

We apply stochastic stability to undiscounted finitely repeated two player games without common interests. We prove an Evolutionary Feasibility Theorem as an analog to the Folk Theorem (Benoit and Krishna, 1985 and 1987). Specifically, we demonstrate that as repetitions go to infinity, the set of stochastically stable equilibrium payoffs converges to the set of individually rational and feasible payoffs. This derivation requires stronger assumptions than the Nash Folk Theorem (Benoit and Krishna, 1987). It is demonstrated that the stochastically stable equilibria are stable as a set, but unstable as individual equilibria. Consequently, the Evolutionary Feasibility Theorem makes no prediction more specific than the entire individually rational and feasible set.

Keywords: evolution; stochastic stability; repeated games

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