A Note on Evolutionary Stability of Bertrand Equilibrium

It is shown that the equilibrium notion of an evolutionary stable strategy (ESS) does have predictive power for standard models of Bertrand competition. This is in contrast to a recent claim by Qin and Stuart (1997). The claim is based on the observation that the solution concept ESS behaves discontinuously when finite (discrete) action games approach an infinite (continuous) action game in the limit. Furthermore, it is argued that from a model-theoretic point of view evolutionary stability in prices (i.e. in the Bertrand model) is quite different from evolutionary stability in quantities (i.e. in the Cournot model)