Heterogeneity stabilizes reciprocal altruism interactions

In considering the phenomena of reciprocal altruism few would dispute that there are differences in individual quality-in particular, that for some individuals, at least on occasion, the cost of doing favors will exceed the potential of future benefits. That is, at any given time, a typical population is heterogeneous with respect to the affordability of reciprocal altruism. However, methodological limitations of the traditional analytical framework-Single Type (symmetric) Evolutionary Game Theory-have restricted previous analytical efforts to addressing populations idealized in terms of their averages. Here we use the methods of Multitype Evolutionary Game Theory to analyse the role of individual differences in direct reciprocity interactions. Multitype analysis shows that non-idealized populations possess an ESS profile wherein individuals who cannot afford reciprocity (low-quality) defect, while individuals who derive net benefits from reciprocity (high-quality) cooperate. Furthermore, this cooperation is implemented via unmodified tit-for-tat (TfT) strategy. Hence, our results may help resolve a long-standing problem concerning the evolutionary stability of TfT in direct reciprocal altruism. Finally, this difference between idealized and real populations is not restricted to direct reciprocal cooperation. Previously (Lotem et al., 1999) we have demonstrated evolutionarily stable indirect reciprocal cooperation among high-quality individuals in heterogeneous populations.