Theoretical Economics, Volume 5, Number 1 (January 2010)

Theoretical Economics 5 (2010), 27–50

Local stability under evolutionary game dynamics

William H. Sandholm


We prove that any regular ESS is asymptotically stable under any impartial pairwise comparison dynamic, including the Smith dynamic; under any separable excess payoff dynamic, including the BNN dynamic; and under the best response dynamic. Combined with existing results for imitative dynamics, our analysis validates the use of ESS as a blanket sufficient condition for local stability under evolutionary game dynamics.

Keywords: Evolutionary game dynamics, ESS

JEL classification: C73

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