The evolutionary stability of cooperation is a problem of fundamental importance for the biological and social sciences. Different claims have been made about this issue: whereas Axelrod and Hamilton's [Axelrod, R. & Hamilton, W. (1981) Science 211, 1390Science 211, -1398] widely recognized conclusion is that cooperative rules such as "tit for tat" are evolutionarily 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 stable in this game. Here we explain why these claims are not contradictory by showing in what sense strategies in the IPD can and cannot be stable and by creating a conceptual framework that yields the type of evolutionary stability attainable in the IPD and in repeated games in general. Having established the relevant concept of stability, we report theorems on some basic properties of strategies that are stable in this sense. We first show that the IPD has "too many" such strategies, so that being stable does not discriminate among behavioral rules. Stable strategies differ, however, on a property that is crucial for their evolutionary survival-the size of the invasion they can resist. This 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 most robust evolutionary equilibrium: the easiest to attain, and the hardest to disrupt.In the last decade, one of the most famous theoretical problems of the biological and social sciences-how humans and other animals can cooperate despite temptations to defecthas attracted much interest. The issue has been approached via a new framework, evolutionary game theory, which has provided one of the most interesting ways of thinking about this problem. However, different claims have been made about the evolutionary stability of cooperation, and these solutions seem to contradict each other. Several well-known though apparently incongruent results have been reported in many renowned books (1-3) and journals (4-8). Clearly, those who claim tit for tat (TFT) to be evolutionarily stable and those who claim it is not cannot both be right-if,.of course, they are using the same concept of stability. Our first objective, then, is to clarify these seemingly contradictory claims by showing in what sense strategies are and are not stable in the iterated prisoner's dilemma (IPD) and other repeated games. Our second objective is to report theorems, within the clarified conceptual framework, that establish some basic properties of strategies which are stable in the IPD.The problem of cooperation among unrelated animals is typically (1, 2, 4-6, 9-11) modeled as a population of individuals engaged in random pairwise prisoner's dilemmas (PDs). The players have a constant probability, w, of meeting in the next period (0 < w < 1). In each period there are twoThe publication costs o...