Evolutionary Selection with Discriminating Players: First draft June 1992. Current version 17 February 1993

Abstract: This paper studies evolutionary games in which players can condition their strategy choice on some observable characteristic of their opponent, a characteristic we call their type. Recently, examples have been provided in which some players discriminate in this way, causing the evolutionary process to converge on non-Nash equilibrium play. Moreover, in some cases this generalization of the standard set-up of evolutionary game theory has been shown to destabilize certain inefficient Nash equilibria. We here provide a general model of evolutionary selection among discriminating behaviors, and find that the above examples are not robust; the close connection between evolutionary selection and Nash equilibrium, already established for the standard set-up, continues to hold, albeit in a slightly more complex form. Moreover, inefficient Nash equilibria may indeed be (weakly) stable in the evolutionary dynamics, and efficient Nash equilibria may be unstable.;