Evolutionarily stable strategies in the repeated prisoner's dilemma

Abstract

Abstract Recently evolutionary game theory has been used in analyzing the repeated prisoner's dilemma and the evolution of cooperation. In this paper Selten's three different ESS definitions in extensive form games are reviewed and applied to the repeated prisoner's dilemma with discounting. It is shown that neither normal form ESS nor direct ESS (in pure or mixed strategies) exists in this game when the players do not make a mistake at any decision node. But when players make an error at every decision node with a small but positive probability, a result analogous to the Folk Theorem can be proved for the limit ESS. Several remarks on the evolutionary interpretation of Axelrod's tournament results follow.