Abstract
Complex networks impact the diffusion of ideas and innovations, the formation of opinions, and the evolution of cooperative behavior. In this context, heterogeneous structures have been shown to generate a coordination-like dynamics that drives a population towards a monomorphic state. In contrast, homogeneous networks tend to result in a stable co-existence of multiple traits in the population. These conclusions have been reached through the analysis of networks with either very high or very low levels of degree heterogeneity. In this paper, we use methods from Evolutionary Game Theory to explore how different levels of degree heterogeneity impact the fate of cooperation in structured populations whose individuals face the Prisoner’s Dilemma. Our results suggest that in large networks a minimum level of heterogeneity is necessary for a society to become evolutionary viable. Moreover, there is an optimal range of heterogeneity levels that maximize the resilience of the society facing an increasing number of social dilemmas. Finally, as the level of degree heterogeneity increases, the evolutionary dominance of either cooperators or defectors in a society increasingly depends on the initial state of a few influential individuals. Our findings imply that neither very unequal nor very equal societies offer the best evolutionary outcome.
Highlights
Previous theoretical works have extensively explored the role of the population structure in the evolution of cooperation
To explore how different levels of degree heterogeneity impact the evolution of cooperation, we make extensive Monte Carlo simulations of the evolutionary dynamics
There is a region in the α × β domain under which the viability of cooperation is more resilient to variations in the harshness of the social dilemma faced by individuals (λ)
Summary
Previous theoretical works have extensively explored the role of the population structure in the evolution of cooperation. Structures with high levels of degree heterogeneity (e.g. scale-free networks) prompt a coordination-like dynamics[36,37] that result in the population being quickly driven to a monomorphic state which is dominated by one of the existing behaviors (i.e. either only cooperators or defectors). In these heterogeneous networks, the observed coordination dynamics results from the existence of higher degree nodes (i.e. hubs) that act as role models and lead to effective dynamics of competition between hubs. Α takes the role of the degree heterogeneity parameter exhibiting a one-to-one relationship with var(z), so that a low (large) α is associated with a low (large) level of degree variance or heterogeneity
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