Evolutionary effects of mobility in ZD strategies for the iterated prisoner’s dilemma game

Abstract

The prisoner's dilemma game has been used widely to address the question of how cooperation emerges among selfish individuals. Press & Dyson (2012) have greatly expanded our understanding of this game by proposing so-called Zero-Determinant (ZD) strategies that impose a fixed linear relationship between one’s own payoff and that of the other. Extortion strategies, a subset of ZD strategies, can have a higher payoff than the opponent, but, as is the same with other ZD strategies, they are not evolutionarily stable as they have a small payoff when playing with themselves. This study investigates the performance of Extortion strategies when they are provided with mobility, in other words, they could continue to play with novel strategies. The experiments show that the proportion of them has a peak when the speed of their movement is moderate, among the population of Extortion, TFT, ALLC and ALLD.