Graph topology plays a determinant role in the evolution of cooperation

Santos, Francisco C.; Rodrigues, José Francisco; Pacheco, Jorge M.

doi:10.1098/rspb.2005.3272

Cited by 329 publications

(270 citation statements)

References 20 publications

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“…As expected, the degree of cooperation c decreases monotonously as the temptation to defect b increases. How- [20]. This is in contrast with the constant decrease of the cooperation observed in networks with no clustering.…”

contrasting

confidence: 53%

“…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 clustering SF networks are studied. Therefore, it is necessary to explore the effects that structural properties such as clustering and degre-degree correlations have on the survival of cooperation in complex netwoks.…”

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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: 53%

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confidence: 99%

Enhancement of cooperation in highly clustered scale-free networks

Assenza¹,

2008

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“…That is, strong social relationships may exist for receiving cooperation from others (Brown and Brown, 2006;Miritello et al, 2013b). However, cooperators cannot cooperate with everyone because there are costs of cooperation (Santos et al, 2006;Xu and Wang, 2015). Actually, human beings tend to cooperate with close friends (Haan et al, 2006;Harrison et al, 2011;Dunbar, 2016).…”

Section: Discussionmentioning

confidence: 99%

Limitations of time resources in human relationships determine social structures

Takano¹,

Fukuda²

2017

Palgrave Commun

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The number of social relationships that a single human being can possibly be involved in is limited because individuals face time constraints (that is, time costs) in constructing and maintaining social relationships; furthermore, the distribution of the strength of such relationships (as measured by frequency of social interaction) looks significantly skewed (a power law distribution), that is, a few strong relationships and many weak relationships. This skewedness suggests that the costs and benefits of bonding with others depend on the strength of the social relationships: if it involves uniform costs and benefits, the distribution would not be skewed. The bonding is known as social grooming; that is, humans strategically construct their social relationships, and thus, complex human societies should also be strategically constructed. Therefore, it is important to know their strategies for understanding human societies. Previous studies provide evidence of social grooming strategies by examining the evolution and the difference between the various social grooming methods. However, quantitative laws that are important for theoretically understanding human societies are still open to investigation. Social big data is a particularly powerful tool for finding such laws. Therefore, we analyse data from six communication systems (Twitter, a social networking site providing two types of interactions, an avatar chat, a mobile phone and a short message service). We find a simple quantitative law by which social relationships are constrained Nm a (a41); here, N is the number of social relationships and m is a mean of the strength of those relationships. The fact that deep social relationships require higher costs per relationship than shallow relationships is suggested by a41 (if the both is equal then a will be 1), because the effect of m on the constraint increases with m. For exploring why a is greater than 1, we conduct an individual-based simulation where social grooming costs are assumed to increase linearly with the strength of social relationships. Our results indicate that this model fits all data sets; that is, it displays an explanation capacity for the phenomenon. In addition, an analysis of this simulation proves our assumption about the social grooming cost increasing with the strength of social relationships as being true. Moreover, it suggests that its gradient increases the width and shallowness of these relationships. The law and its causes suggest that mankind's evolution of social grooming has enabled changing social structures, and the phenomenon is because of the constraints of the social network generation. These findings will contribute towards an explanation of the evolution of the various social grooming methods of humans and their significantly large social group.

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“…Studies of metaphors for this problem, such as the Prisoner's Dilemma (PD), seem to me mostly to give useful answers only under implausibly restrictive assumptions (reviewed in [50]). A blend of network dynamics with PD metaphors might provide more robust answers to this question [51,52]. I end as I began, with the network structure of species interacting in food webs and ecosystems.…”

Section: Network Structure and Infectious Disease Dynamicsmentioning

confidence: 99%