Natural selection of cooperation and degree hierarchy in heterogeneous populations

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

doi:10.1016/j.jtbi.2008.03.007

Cited by 56 publications

(44 citation statements)

References 22 publications

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“…It is noteworthy that our results remain qualitatively valid for other update rules, such as the discrete analogue of the replicator dynamics on graphs, used in many references, e.g., [16], [27], [38], [65]. In fact, the AGoS is capable of identifying particular features of such dynamics: For instance, the partially deterministic nature of such update rule may lead to evolutionary deadlocks in heterogeneous (scale-free) networks, creating stationary states close to full cooperation [16], [27]. In such situation, the AGoS will reflect the occurrence of these stationary configurations by shifting to the left-hand side the stable ( x R ) equilibrium , which may no longer coincide with j = N , remaining, however, in its vicinity.…”

Section: Resultssupporting

confidence: 72%

From Local to Global Dilemmas in Social Networks

2012

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Social networks affect in such a fundamental way the dynamics of the population they support that the global, population-wide behavior that one observes often bears no relation to the individual processes it stems from. Up to now, linking the global networked dynamics to such individual mechanisms has remained elusive. Here we study the evolution of cooperation in networked populations and let individuals interact via a 2-person Prisoner's Dilemma – a characteristic defection dominant social dilemma of cooperation. We show how homogeneous networks transform a Prisoner's Dilemma into a population-wide evolutionary dynamics that promotes the coexistence between cooperators and defectors, while heterogeneous networks promote their coordination. To this end, we define a dynamic variable that allows us to track the self-organization of cooperators when co-evolving with defectors in networked populations. Using the same variable, we show how the global dynamics — and effective dilemma — co-evolves with the motifs of cooperators in the population, the overall emergence of cooperation depending sensitively on this co-evolution.

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Section: Resultssupporting

confidence: 72%

From Local to Global Dilemmas in Social Networks

2012

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“…If such a local strategic configuration arises, as it is indeed the case discussed here, then neither of the two hubs will take over the set of fluctuating individuals, nor the latter will invade the hubs as they are mainly lowly connected nodes with small payoffs. This can be understood in terms of the so-called dipole model [16,25], that shows analytically that two hubs with opposite strategies can coexist as we have just described. In particular, it can be argued that, in addition to fluctuating nodes, cooperator hubs should also have a set of cooperators linked to them, for this will provide the hubs with a stable source of benefits.…”

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confidence: 83%

“…The reason behind the increase of cooperation levels in scale-free networks is that hubs are occupied by cooperators, which ensures their long term success and higher levels of cooperation in the network. In fact, the probability that a node of degree k plays as a cooperator increases with k [16], which leads to an organization of cooperation in scale-free networks radically distinct from that of homogeneous topologies [11].…”

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confidence: 99%

Cooperative scale-free networks despite the presence of defector hubs

et al. 2009

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PACS 89.75.Fb -Structures and organization in complex systems PACS 87.23.Kg -Dynamics of evolution PACS 89.65.-s -Social and economic systems Abstract -Recent results have shown that heterogeneous populations are better suited to support cooperation than homogeneous settings when the Prisoner's Dilemma drives the evolutionary dynamics of the system. The same occurs when the network growth is coevolving together with the evolutionary dynamics, which also gives rise to highly cooperative scale-free networks. In the latter case, however, the organization of cooperation is radically different with respect to the case in which the underlying network is static. In this paper we study the structure of cooperation in static networks grown together with evolutionary dynamics and show that the general belief that hubs can only be occupied by cooperators does not hold. Moreover, these scale-free networks support high levels of cooperation despite having defector hubs. Our results have several important implications for the explanation of cooperative behavior in scale-free networks and highlight the importance that the formation of complex systems have on its function.Evolutionary dynamics [1] has attracted a lot of interest in the physics community lately, in particular in the context of evolutionary games on graphs [2,3]. This is a most relevant problem both from the physics viewpoint as well as from its applications. Indeed, evolutionary games describe a local optimization dynamics, which is largely different from the hamiltonian dynamics that is the traditional physics paradigm. On the other hand, these problems are related to important biological and socioeconomical issues, such as the emergence of cooperation [4].To date, a great deal of work has been done on evolutionary game dynamics on fixed networks (see, e.g., [2] and references therein). Beginning with the pioneering work by Nowak and May [5], much research has focused on whether the chances of establishing cooperative behavior (if not global, at least to a large extent) are improved by (a)

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“…This description has been already introduced in [24] for BA networks. Obviously, the value k * (b) grows with b (see Fig.3.a) and hence the conversion of cooperator into defector strategies can be explained as a progressive invasion of the degree classes by defectors: the larger the value of b the more degree hierarchies defectors have invaded.…”

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confidence: 99%

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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Natural selection of cooperation and degree hierarchy in heterogeneous populations

Cited by 56 publications

References 22 publications

From Local to Global Dilemmas in Social Networks

From Local to Global Dilemmas in Social Networks

Cooperative scale-free networks despite the presence of defector hubs

Enhancement of cooperation in highly clustered scale-free networks

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