TYPES OF EVOLUTIONARY STABILITY AND THE PROBLEM OF COOPERATION

The evolutionary stability of cooperation is a problem of fundamental importance for the biological and social sciences. Different claims ha ve been made about this issue: whereas Axelrod and Hamilton's [Axelrod , R. and Hamilton, W. (1981) Science 211, 1390-1398] widely recognized conclusion is that cooperative rules such as ''tit for tat'' are evol utionarily stable strategies in the iterated prisoner's dilemma (IPD), Boyd and Lorberbaum [Boyd, R. & Lorberbaum, J. (1987) Nature (London) 327, 58-59] have claimed that no pure strategy is evolutionarily stab le in this game. Here we explain why these claims are not contradictor y by showing in what sense strategies in the IPD can and cannot be sta ble and by creating a conceptual framework that yields the type of evo lutionary stability attainable in the IPD and in repeated games in gen eral. Having established the relevant concept of stability, we report the!orems on some basic properties of strategies that are stable in th is sense. We first show that the IPD has ''too many'' such strategies, so that being stable does not discriminate among behavioral rules. St able strategies differ, however, on a property that is crucial for the ir evolutionary survival-the size of the invasion they can resist. Thi s property can be interpreted as a strategy's evolutionary robustness. Conditionally cooperative strategies such as tit for tat are the most robust. Cooperative behavior supported by these strategies is the mos t robust evolutionary equilibrium: the easiest to attain, and the hard est to disrupt.