Conformity and network effects in the Prisoner's Dilemma

We study the evolution of cooperation using the Prisoner's Dilemma as a metaphor of the tensions between cooperators and non-cooperators, and evolutionary game theory as the mathematical framework for modeling the cultural evolutionary dynamics of imitation in a population of unrelated individuals. We investigate the interplay between network reciprocity (a mechanism that promotes cooperation in the Prisoner's Dilemma by restricting interactions to adjacent sites in spatial structures or neighbors in social networks) and conformity (the tendency of imitating common behaviors). We confirm previous results on the improved levels of cooperation when both network reciprocity and conformity are present in the model and evolution is carried on top of degree-homogeneous graphs, such as rings and grids. However, we also find that scale-free networks are no longer powerful amplifiers of cooperation when fair amounts of conformity are introduced in the imitation rules of the players. Such weakening of the cooperation-promoting abilities of scale-free networks is the result of a less biased flow of information in such topologies, making hubs more susceptible of being influenced by lessconnected neighbors.

I Introduction

Cooperation is ubiquitous in nature. From replicating molecules to humans, individuals cooperate with others even when such an option represents a cost to themselves. For this reason, understanding the emergence of cooperation is a central problem in many fields of both natural and social sciences, such as biology, sociology, anthropology and economics. Researchers of such diverse disciplines have traditionally adopted the Prisoner's Dilemma (PD) as metaphor for the tension between group welfare and individual self-ishness, and evolutionary game theory [1], [2] as a common formal framework for studying both genetic and cultural evolution.