  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.
