2013), Evolution of extortion in Iterated Prisoner's Dilemma games

Iterated games are a fundamental component of economic and evolution-ary game theory. They describe situations where two players interact re-peatedly and have the ability to use conditional strategies that depend on the outcome of previous interactions, thus allowing for reciprocation. Recently a new class of strategies has been proposed, so called ‘zero determinant strate-gies’. These strategies enforce a fixed linear relationship between one’s own payoff and that of the other player. A subset of those strategies allows ‘ex-tortioners ’ to ensure that any increase in the own payoff exceeds that of the other player by a fixed percentage. Here we analyze the evolutionary per-formance of this new class of strategies. We show that in reasonably large populations they can act as catalysts for the evolution of cooperation, similar to tit-for-tat, but that they are not the stable outcome of natural selection. In very small populations, however, extortioners hold their ground. Extortion strategies do particularly well in co-evolutionary arms races between two dis-tinct populations: significantly, they benefit the population which evolves at the slower rate- an instance of the so-called Red King effect. This may affect the evolution of interactions between host species and their endosymbionts