Abstract In biology, there is often a tension between what is good for the individual and what is good for the population (1–6). Cooperation benefits the community, while defection tempts the individual to garner short term gains. The theory of repeated games specifies that there is a continuum of Nash equilibria which ranges from fully defective to fully cooperative (7,8). The mechanism of direct reciprocity, which relies on repeated interactions, therefore only stipulates that evolution of cooperation is possible, but whether or not cooperation can be established, and for which parameters, depends on the details of the underlying process of mutation and selection (9–18). Many well known evolutionary processes achieve cooperation only in restricted settings. In the case of the donation game (5,6), for example, high benefit to-cost ratios are often needed for selection to favor cooperation (19–22). Here we study a universe of two-player cooperative dilemmas (23), which includes the prisoner’s dilemma (24–27), snowdrift (28–30), stag-hunt (31) and harmony game. Upon those games we apply a universe of evolutionary processes. Among those processes we find a continuous set which has the feature that it achieves maximum payoff for all cooperative dilemmas under direct reciprocity. This set is characterized by a surprisingly simple property which we call parity: competing strategies are evaluated symmetrically.
LaPorte et al. (2025) studied this question.