Dynamic Motifs of Strategies in Prisoner's Dilemma Games

TL;DR

This paper introduces dynamic motifs as a novel way to analyze and visualize the complex strategy interactions in iterated prisoner's dilemma games, revealing fundamental building blocks of strategic dynamics.

Contribution

It presents the concept of dynamic motifs, identifies 22 such motifs through enumeration, and demonstrates their utility in simplifying and understanding complex strategic behaviors.

Findings

Identification of 22 dynamic motifs in strategy interactions.

Visualization of phase portraits for each motif.

Dynamic motifs serve as fundamental units for understanding strategy dynamics.

Abstract

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.