Enhancement of cooperation in highly clustered scale-free networks

Abstract

We study the effect of clustering on the organization of cooperation, by analyzing the evolutionary dynamics of the Prisoner's Dilemma on scale-free networks with a tunable value of clustering. We find that a high value of the clustering coefficient produces an overall enhancement of cooperation in the network, even for a very high temptation to defect. On the other hand, high clustering homogeneizes the process of invasion of degree classes by defectors, decreasing the chances of survival of low densities of cooperator strategists in the network.PACS numbers: 87.23.Ge, 02.50. Le, 89.75.Fb Cooperative phenomena are essential in natural and human systems and have been the subject of intense research during decades [1,2,3,4,5,6]. Evolutionary game theory is concerned with systems of replicating agents programmed to use some strategy in their interactions with other agents, which ultimately yields a feedback loop that drives the evolution of the strategies composition of the population [6,7,8]. To understand the observed survival of cooperation among unrelated individuals in populations when selfish actions provide a short-term higher benefit, a lot of attention has been paid to the analysis of evolutionary dynamics of the Prisoner's Dilemma (PD) game. In this simple two-players game, individuals adopt one of the two available strategies, cooperation (C) or defection (D); both receive R under mutual cooperation and P under mutual defection, while a cooperator receives S when confronted to a defector, which in turn receives T , where T > R > P > S. Under these conditions in a one-shot game it is better to defect, regardless of the opponent strategy, and the proportion of cooperators asymptotically vanishes in a well-mixed population. On the other hand, the structure of interactions among individuals in real societies are seen to be described by complex networks of contacts rather than by a set of agents connected all-to-all [9,10]. Therefore, it is necessary to abandon the panmixia hypothesis to study how cooperative behavior appear in the social context.Several studies [11,12,13,14,15,16,17,18,19] have reported the asymptotic survival of cooperation on different kinds of networks. Notably, cooperation even dominates over defection in non-homogeneous, scale-free (SF) networks, i.e. in graphs where the number k of neighbors of an individual (the node degree) is distributed as a power law [12,15], P (k) ∼ k −γ , with 2 < γ ≤ 3. Networks with such a distribution are ubiquitous: scale-free topologies appear as the backbone of many social, biological, technological complex systems. However, in the context of social systems, other topological features, such as the presence of degree-degree correlations and of high clustering coefficients, are relevant ingredients to take into account in a complete description of the networks. The studies of the PD game on SF networks have considered so far networks with no degree correlations and nearly zero clustering coefficient, with the remarkable exception of Ref. [20] where high ...

Effects of mobility in a population of prisoner’s dilemma players

“…Indeed, the graph corresponds to a random geometric graph [20], a network having the same P (k) as an ER random graph, but with a higher clustering coefficient. This latter feature leads to a further increment of the average level of cooperation, as it has been shown that a network with a high clustering coefficient promotes cooperation [21,22].…”

Effects of asynchronism on evolutionary games

“…While small-world networks are also known to support cooperative behaviors (Abramson and Kuperman, 2001;6 Tomassini et al, 2006;Vukov et al, 2008), it has been extensively reported that scale-free networks strongly enhance the survival of cooperation Santos et al, , 2006Gómez-Gardeñes et al, 2007. Different aspects related to social structure have been studied such as, for example, clustering (Assenza et al, 2008), robustness to suppression of nodes (Perc, 2009), the existence of distinct interaction and updating neighborhoods (Ohtsuki et al, 2007), as well as the interplay between social structure and other aspects such as diversity of reproduction rates (Szolnoki et al, 2008c) and payoff normalization (Tomassini et al, 2007;Szolnoki et al, 2008b). Besides features related to social structure, as spatial distance and heterogeneity in the number of connections, it is commonly accepted that relatedness of individuals, reputation and repeated interactions, allied to memory and recognition capacities, are also mechanisms that promote cooperative behaviors (Axelrod, 1984).…”

Quantum strategies win in a defector-dominated population

“…It is known that the structure of the network is also a key factor in the evolution of behavior of agents. Later, a shift from evolutionary games on regular lattices to evolutionary games on complex networks was proposed [5], in particular on small world networks [6,7,8] and on scale-free networks [9,10,11]. Meanwhile, other games, such as Snowdrift (SD) [12], Stag-Hunt (SH) [13], and Public Goods games, have produced interesting results [14,15,16,17].…”