Iterated prisoner's dilemma with extortionate zero-determinant strategies and random-memory opponents

摘要

We investigate Extortionate Zero Determinant (EZD) strategies for the iterated prisoner's dilemma (IPD) against random memory-based strategies without mutation. These strategies are randomly-generated deterministic instructions with a predetermined average level of cooperation. While EZD strategies generally outperform any single evolutionary opponent, we show that under certain conditions EZD strategies can be taken over by a small number of randomly-generated deterministic strategies and force the EZD to extinction. We demonstrate that a major determining factor contributing to this phenomena is the maximum score among all non-EZD strategies when playing against itself. In contrast, we theoretically analyze the IPD consisting of an EZD strategy and a purely random one that cooperates each round with a predetermined probability. In this latter case, the EZD almost always prevails though the purely random player survives. In this sense, we conclude that even without mutation, it is still evolutionarily advantageous for the IPD to have a diverse initial random population.