From extortion to generosity, evolution in the Iterated Prisoner’s Dilemma

Significance Cooperative behavior seems at odds with the Darwinian principle of survival of the fittest, yet cooperation is abundant in nature. Scientists have used the Prisoner Dilemma game, in which players must choose to cooperate or defect, to study the emergence and stability of cooperation. Recent work has uncovered a remarkable class of extortion strategies that provide one player a disproportionate payoff when facing an unwitting opponent. Extortion strategies perform very well in head-to-head competitions, but they fare poorly in large, evolving populations. Rather we identify a closely related set of generous strategies, which cooperate with others and forgive defection, that replace extortionists and dominate in large populations. Our results help to explain the evolution of cooperation. Recent work has revealed a new class of “zero-determinant” (ZD) strategies for iterated, two-player games. ZD strategies allow a player to unilaterally enforce a linear relationship between her score and her opponent’s score, and thus to achieve an unusual degree of control over both players’ long-term payoffs. Although originally conceived in the context of classical two-player game theory, ZD strategies also have consequences in evolving populations of players. Here, we explore the evolutionary prospects for ZD strategies in the Iterated Prisoner’s Dilemma (IPD). Several recent studies have focused on the evolution of “extortion strategies,” a subset of ZD strategies, and have found them to be unsuccessful in populations. Nevertheless, we identify a different subset of ZD strategies, called “generous ZD strategies,” that forgive defecting opponents but nonetheless dominate in evolving populations. For all but the smallest population sizes, generous ZD strategies are not only robust to being replaced by other strategies but can selectively replace any noncooperative ZD strategy. Generous strategies can be generalized beyond the space of ZD strategies, and they remain robust to invasion. When evolution occurs on the full set of all IPD strategies, selection disproportionately favors these generous strategies. In some regimes, generous strategies outperform even the most successful of the well-known IPD strategies, including win-stay-lose-shift.