  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.
