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Dynamic Motifs of Strategies in Prisoner's Dilemma Games

We investigate the win-lose relations between strategies of iterated prisoner's dilemma games by using a directed network concept to display the replicator dynamics results. In the giant strongly-connected component of the win/lose network, we find win-lose circulations similar to rock-paper-scissors and analyze the fixed point and its stability. Applying the network motif concept, we introduce dynamic motifs, which describe the population dynamics relations among the three strategies. Through exact enumeration, we find 22 dynamic motifs and display their phase portraits. Visualization using directed networks and motif analysis is a useful method to make complex dynamic behavior simple in order to understand it more intuitively. Dynamic motifs can be building blocks for dynamic behavior among strategies when they are applied to other types of games.