From extortion to generosity, the evolution of zero-determinant strategies in the prisoner's dilemma

Abstract

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 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 zero-determinant strategies - and 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 they also can selectively replace any non-cooperative 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 Iterated Prisoner's Dilemma strategies, including win-stay-lose-shift.

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