Seed-Dependent Fixation of Cooperation in Structured Populations

Abstract

The spatial structure of populations plays a decisive role in shaping the evolution of cooperation. Within the framework of evolutionary game theory, we explore the subtle role of structural reciprocity, the correlation between network architecture and cooperative dynamics. Using numerical experiments on ensembles of populations with diverse structural characteristics, we show that degree–degree correlations and the power-law exponent of degree distributions significantly affect the classical mechanism of spatial reciprocity. Special emphasis is placed on the attributes of the initial (seed) cooperator that determine the likelihood of cooperation fixation. Our results reveal that the degree of the seed cooperator can either promote or inhibit cooperation depending on the payoff parameters, but network architectures with low average degree, degree homogeneity, and negative degree–degree correlations consistently provide fertile ground for cooperation to emerge and persist. These findings highlight the nuanced interplay between initial conditions and structural features in governing the evolutionary success of cooperative strategies.