A Novel Technique for Quantifying Clusters Based on Small Squares in a Spatial Prisoner's Dilemma.

Abstract A number of studies have revealed and investigated how the clusters organized by cooperators emerge in a spatial prisoner’s dilemma. However, a qualitative analysis of the clusters formed by the cooperators has not yet been studied. This paper aims to propose a new technique for quantifying clusters that consist of players with cooperative strategies. The proposed method can be applied to the spatial prisoner’s dilemma in a square lattice network. In the proposed method, a minimum cluster is defined as a group of the cooperators based on a small square (2 by 2). This paper also defines a degree of the clusters by extending the small squares that based on how the players organize themselves into coordinated groups. The authors analyze and compare with typical examples of the clusters in the spatial prisoner’s dilemma. By analyzing the examples, this paper demonstrates that the proposed method quantifies the degree of the clusters organized by the cooperators. The authors also examine the significance of the proposed method by the simulations of the spatial prisoner’s dilemma.