Evolutionarily Stable Strategies in the Prisoner’s Dilemma and Chicken Games

Abstract

In a famous paper, Robert Axelrod (1981) has presented an analysis of the evolution of cooperative behaviour among self interested individuals. His analysis is of the iterated prisoner’s dilemma game; he shows that under certain conditions the tit-for-tat strategy (i.e. cooperate on your first move, then always repeat your opponent’s last move) is a ‘collectively stable strategy’. In this paper I shall extend Axelrod’s work in two main ways. First, I shall analyse a two-person game which encompasses the prisoner’s dilemma as a special case; the chicken game is another special case. Second, I shall argue that Axelrod’s concept of a ‘collectively stable strategy’ is a concept of equilibrium but not of stability. A more satisfactory concept, of an evolutionarily stable strategy (ESS) is widely used in theoretical biology; I shall use this. In order to identify ESSs I shall allow for the possibility that players make occasional mistakes.