Impact of topology on the dynamical organization of cooperation in the prisoner’s dilemma game

Pusch, Andreas; Weber, Sebastian; Porto, Markus

doi:10.1103/physreve.77.036120

Cited by 82 publications

(51 citation statements)

References 23 publications

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“…Recent reviews [8][9][10][11] clearly attest to the fact that physics-inspired research has helped refine many of these concepts. In particular, evolutionary games in networks, spurred on by the seminal discovery of spatial reciprocity [12] and, subsequently, * szolnoki.attila@ttk.mta.hu by the discovery that scale-free networks strongly facilitate the evolution of cooperation [13,14], are still receiving ample attention to this day [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. One of the most recent contributions to the subject concerns the assignment of cognitive skills to individuals that engage in evolutionary games in networks [35,[38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas

Szolnoki

Xie

et al. 2013

Phys. Rev. E

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We show that the resolution of social dilemmas in random graphs and scale-free networks is facilitated by imitating not the strategy of better-performing players but, rather, their emotions. We assume sympathy and envy to be the two emotions that determine the strategy of each player in any given interaction, and we define them as the probabilities of cooperating with players having a lower and a higher payoff, respectively. Starting with a population where all possible combinations of the two emotions are available, the evolutionary process leads to a spontaneous fixation to a single emotional profile that is eventually adopted by all players. However, this emotional profile depends not only on the payoffs but also on the heterogeneity of the interaction network. Homogeneous networks, such as lattices and regular random graphs, lead to fixations that are characterized by high sympathy and high envy, while heterogeneous networks lead to low or modest sympathy but also low envy. Our results thus suggest that public emotions and the propensity to cooperate at large depend, and are in fact determined by, the properties of the interaction network.

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Section: Introductionmentioning

confidence: 99%

Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas

Szolnoki

Xie

et al. 2013

Phys. Rev. E

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“…In fact, both reports are correct in so far as, as has been shown recently (see [3,9] and references therein), the outcome of evolutionary games on these graphs is largely dependent on the model details (such as evolutionary update rule, network clustering, etc.). For degreeheterogeneous networks, and in particular for scale-free (SF) networks [10], there are grounds to claim an improvement of cooperation at least in some parameter regions [11][12][13][14][15]. 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.…”

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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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“…-Importantly, we can study the percolation properties of our model analytically, thus extending previous results [3,6,8,11] to more general cases. Let D(s|k) be the probability that a vertex of generalized degree k is a member of a set of s mutually reachable vertices.…”

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confidence: 83%

“…It is thus possible to choose P (k) in order to reproduce both p(k) andc(k) as in other models [2,3,8].…”

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confidence: 99%

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Networks with arbitrary edge multiplicities

Zlatić¹,

Garlaschelli²,

Caldarelli³

2012

EPL

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-One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of triangles in which edges, rather than vertices, participate. Here we show that the multiplicity distribution of real networks is in many cases scale-free, and in general very broad. Thus, besides the fact that in real networks the number of edges attached to vertices often has a scale-free distribution, we find that the number of triangles attached to edges can have a scale-free distribution as well. We show that current models, even when they generate clustered networks, systematically fail to reproduce the observed multiplicity distributions. We therefore propose a generalized model that can reproduce networks with arbitrary distributions of vertex degrees and edge multiplicities, and study many of its properties analytically.Introduction. -Real networks, where nodes (or vertices) are intricately connected by links (or edges), are characterized by complex topological properties such as a scale-free distribution of the degree (number of edges reaching a vertex), degree-degree correlations, and nonvanishing degree-dependent clustering (density of triangles reaching a vertex) [1]. Understanding the structural and dynamical properties of complex networks strongly relies on the possibility to investigate theoretical models which are both realistic and analytically solvable. Several analytically solvable models reproducing the most important local property of real networks, i.e. the degree distribution, have been proposed [1]. However, models reproducing higher-order properties including clustering (also called transitivity) are only a few and are either entirely computational [2,3] (i.e. not analytically solvable) or solvable only for particular cases, e.g. when triangles are non-overlapping [4][5][6][7] or when the network is made by cliques [8] or other subgraphs [9] embedded in a treelike skeleton. Unfortunately, real networks generally violate the above particular conditions, as empirical analyses have revealed and as we will further show in what follows.

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Impact of topology on the dynamical organization of cooperation in the prisoner’s dilemma game

Cited by 82 publications

References 23 publications

Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas

Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas

Cooperative scale-free networks despite the presence of defector hubs

Networks with arbitrary edge multiplicities

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