Cooperation Prevails When Individuals Adjust Their Social Ties

Abstract

Conventional evolutionary game theory predicts that natural selection favours the selfish and strong even though cooperative interactions thrive at all levels of organization in living systems. Recent investigations demonstrated that a limiting factor for the evolution of cooperative interactions is the way in which they are organized, cooperators becoming evolutionarily competitive whenever individuals are constrained to interact with few others along the edges of networks with low average connectivity. Despite this insight, the conundrum of cooperation remains since recent empirical data shows that real networks exhibit typically high average connectivity and associated single-to-broad–scale heterogeneity. Here, a computational model is constructed in which individuals are able to self-organize both their strategy and their social ties throughout evolution, based exclusively on their self-interest. We show that the entangled evolution of individual strategy and network structure constitutes a key mechanism for the sustainability of cooperation in social networks. For a given average connectivity of the population, there is a critical value for the ratio W between the time scales associated with the evolution of strategy and of structure above which cooperators wipe out defectors. Moreover, the emerging social networks exhibit an overall heterogeneity that accounts very well for the diversity of patterns recently found in acquired data on social networks. Finally, heterogeneity is found to become maximal when W reaches its critical value. These results show that simple topological dynamics reflecting the individual capacity for self-organization of social ties can produce realistic networks of high average connectivity with associated single-to-broad–scale heterogeneity. On the other hand, they show that cooperation cannot evolve as a result of “social viscosity” alone in heterogeneous networks with high average connectivity, requiring the additional mechanism of topological co-evolution to ensure the survival of cooperative behaviour.

Coalitions in theory and reality: a review of pertinent variables and processes

“…Third, the theory of dynamic linking and network formation focuses on dyadic or polyadic games played by individuals in which the outcomes of previous interactions determine who interacts with whom in the future (Skyrms & Pemantle, 2000;Pemantle & Skyrms, 2004a, b;Hruschka & Henrich, 2006;Pacheco et al, 2006Pacheco et al, , 2008Santos et al, 2006;Gavrilets et al, 2008;Aktipis, 2011). We discuss one application of this theory below.…”

Evolutionary Prisoner’s Dilemma Game in Flocks

“…However, the sizes of social networks continuously change in real world as individuals join or quit, and the topologies also evolve as links are created or broken. To capture the dynamic feature of social systems, the evolution of network structure can be coupled with game dynamics through adaptive local interactions, where individuals may adjust social ties according to their payoff [14,15]. But structure dynamics of some networks are directly caused by the movement of individuals.…”

Promotion of cooperation induced by the interplay between structure and game dynamics

“…More recently, Ref. [22] proposed another minimal model that combined strategy evolution with topological evolution. They used asynchronous update rule both for evolution of strategy and structure by the Fermi function.…”

“…Indeed, individuals have adaptations on the number, frequency, and duration of their social ties base upon some certain feedback mechanisms. Instead of investigating the evolutionary games on static networks which constitute just one snapshot of the real evolving ones, recently, some researchers proposed that the network structure may co-evolve with the evolutionary game dynamics [17,18,19,20,21,22,23]. Interestingly, as pointed out in Refs.…”

“…Interestingly, as pointed out in Refs. [18,19,22], the entangled evolution of individual strategy and network structure constitutes a key mechanism for the sustainability of cooperation in social networks. Therefore, to understand the emergence of cooperative behavior in realistic situations (networks), one should combine strategy evolution with topological evolution.…”