Network Structures between Strategies in Iterated Prisoners' Dilemma Games

We use replicator dynamics to study an iterated prisoners' dilemma game with memory. In this study, we investigate the characteristics of all 32 possible strategies with a single-step memory by observing the results when each strategy encounters another one. Based on these results, we define similarity measures between the 32 strategies and perform a network analysis of the relationship between the strategies by constructing a strategies network. Interestingly, we find that a win-lose circulation, like rock-paper-scissors, exists between strategies and that the circulation results from one unusual strategy.