Robustness of cooperation in the evolutionary prisoner's dilemma on complex networks

Poncela, Julia; Gómez‐Gardeñes, Jesús; Floría, L. M.; Moreno, Yamir

doi:10.1088/1367-2630/9/6/184

Cited by 161 publications

(121 citation statements)

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“…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.…”

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confidence: 99%

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Enhancement of cooperation in highly clustered scale-free networks

Assenza¹,

2008

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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 ...

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confidence: 99%

“…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.…”

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confidence: 99%

Enhancement of cooperation in highly clustered scale-free networks

Assenza¹,

2008

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“…Rather, they have a degree distribution with a heavy tail, where many nodes have low degrees, but very few nodes have a very high degree each. In the field of evolutionary game theory inhomogenous graphs have been successfully used to study the evolution of cooperation [4,17,[47][48][49][50], but the impact of changing the updating rule on these results is not fully clear.…”

Section: Discussionmentioning

confidence: 99%

“…The link dynamics updating rule (LD) [17] arose from the study of structured populations and focuses on pairwise interactions. In most cases, a population structure is given in terms of a (static) graph [18], in which nodes correspond to individuals in the population.…”

Section: Introductionmentioning

confidence: 99%

Nonequivalence of updating rules in evolutionary games under high mutation rates

et al. 2014

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Moran processes are often used to model selection in evolutionary simulations. The updating rule in Moran processes is a birth-death process, i. e., selection according to fitness of an individual to give birth, followed by the death of a random individual. For well-mixed populations with only two strategies this updating rule is known to be equivalent to selecting unfit individuals for death and then selecting randomly for procreation (biased death-birth process). It is, however, known that this equivalence does not hold when considering structured populations. Here we study whether changing the updating rule can also have an effect in well-mixed populations in the presence of more than two strategies and high mutation rates. We find, using three models from different areas of evolutionary simulation, that the choice of updating rule can change model results. We show, e. g., that going from the birth-death process to the death-birth process can change a public goods game with punishment from containing mostly defectors to having a majority of cooperative strategies. From the examples given we derive guidelines indicating when the choice of the updating rule can be expected to have an impact on the results of the model.

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“…In this section, we address the opposite case of highly heterogeneous networks, taking scale-free networks (Albert & Barabási, 2002) as our working example. Recent work has pointed out that these networks can be favorable to cooperation (Santos, Pacheco, & Lenaerts, 2006;Poncela, Gó mez-Gardeñ nes, Floría, & Moreno, 2007) and can even self-organize if they grow by incorporating new individuals who choose their neighbors depending on the payoffs of a game (Poncela, Gó mez-Gardeñ nes, Floría, Sán-chez, & Moreno, 2008). Therefore, analyzing the micro-macro link on degree heterogeneous networks is an important subject that deserves attention both on its own and for its possible applications.…”

Section: Degree-heterogeneous Populationsmentioning

confidence: 99%