The Evolution of Extortion in Iterated Prisoner's Dilemma Games

TL;DR

This paper investigates the role and effectiveness of zero determinant extortion strategies in iterated Prisoner's Dilemma games, revealing their potential to promote cooperation and their dynamics in different population sizes and evolutionary contexts.

Contribution

It provides a comprehensive analysis of the evolutionary dynamics of extortion strategies, highlighting their catalytic role in cooperation and their advantage in co-evolutionary arms races.

Findings

Extortion strategies can catalyze cooperation in large populations.

They are not evolutionarily stable under natural selection.

Extortioners perform well in small populations and co-evolutionary arms races.

Abstract

Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the possibility to use conditional strategies that depend on the outcome of previous interactions. In the context of evolution of cooperation, repeated games represent the mechanism of reciprocation. Recently a new class of strategies has been proposed, so called 'zero determinant strategies'. These strategies enforce a fixed linear relationship between one's own payoff and that of the other player. A subset of those strategies are 'extortioners' which ensure that any increase in the own payoff exceeds that of the other player by a fixed percentage. Here we analyze the evolutionary performance 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 they are not the stable outcome of natural selection. In very small populations, however, relative payoff differences between two players in a contest matter, and extortioners hold their ground. Extortion strategies do particularly well in co-evolutionary arms races between two distinct 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.