Voter model dynamics in complex networks: Role of dimensionality, disorder, and degree distribution

Suchecki, Krzysztof; Eguı́luz, Vı́ctor M.; Miguel, M. San

doi:10.1103/physreve.72.036132

Cited by 240 publications

(232 citation statements)

References 45 publications

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“…In high dimensional lattices (d 3) and random networks, the VM dynamics drives the system to a disordered active state, whose proportion of opinions (in our case, actions) is given by the initial conditions [1,31]. This state is dynamic in the ensemble average; the opinion of the agents keeps changing along time.…”

Section: Model Descriptionmentioning

confidence: 99%

Social imitation versus strategic choice, or consensus versus cooperation, in the networked Prisoner's Dilemma

et al. 2014

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The interplay of social and strategic motivations in human interactions is a largely unexplored topic in collective social phenomena. Whether individuals' decisions are taken in a purely strategic basis or due to social pressure without a rational background crucially influences the model outcome. Here we study a networked Prisoner's Dilemma in which decisions are made either based on the replication of the most successful neighbor's strategy (unconditional imitation) or by pure social imitation following an update rule inspired by the voter model. The main effects of the voter dynamics are an enhancement of the final consensus, i.e., asymptotic states are generally uniform, and a promotion of cooperation in certain regions of the parameter space as compared to the outcome of purely strategic updates. Thus, voter dynamics acts as an interface noise and has a similar effect as a pure random noise; furthermore, its influence is mostly independent of the network heterogeneity. When strategic decisions are made following other update rules such as the replicator or Moran processes, the dynamic mixed state found under unconditional imitation for some parameters disappears, but an increase of cooperation in certain parameter regions is still observed. Comparing our results with recent experiments on the Prisoner's Dilemma, we conclude that such a mixed dynamics may explain moody conditional cooperation among the agents.

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Section: Model Descriptionmentioning

confidence: 99%

Social imitation versus strategic choice, or consensus versus cooperation, in the networked Prisoner's Dilemma

et al. 2014

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“…The Voter Model has become an emblematic opinion spreading model due to its simplicity and tractability, as well as its distinction from other coarsening phenomena such as the Ising model [11]. The original Voter Model has been extended to include network structure [12,13,14] and the effect of changes in the microscopic interactions [15,16]. Masuda et al investigated the effect of heterogeneity in the flip-rates of agents [17].…”

Section: Introductionmentioning

confidence: 99%

A voter model with time dependent flip rates

Baxter¹

2011

J. Stat. Mech.

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Abstract. We introduce time variation in the flip-rates of the Voter Model. This type of generalisation is relevant to models of ageing in language change, allowing the representation of changes in speakers' learning rates over their lifetime. and may be applied to any other similar model in which interaction rates at the microscopic level change with time. The mean time taken to reach consensus varies in a nontrivial way with the rate of change of the flip-rates, varying between bounds given by the mean consensus times for for static homogeneous (the original Voter Model) and static heterogeneous flip-rates. By considering the mean time between interactions for each agent, we derive excellent estimates of the mean consensus times and exit probabilities for any time scale of flip-rate variation. The scaling of consensus times with population size on complex networks is correctly predicted, and is as would be expected for the ordinary voter model. Heterogeneity in the initial distribution of opinions has a strong effect, considerably reducing the mean time to consensus, while increasing the probability of survival of the opinion which initially occupies the most slowly changing agents. The mean times to reach consensus for different states are very different. An opinion originally held by the fastest changing agents has a smaller chance to succeed, and takes much longer to do so than an evenly distributed opinion.

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“…The voter model has been extensively studied on lattices [1] and, in recent years, on complex networks [2][3][4][5][6] and is closely related to models of language evolution [7], ecological dynamics [8], opinion dynamics [9], and epidemic spread [10]. The voter model defines a dynamical process where nodes are each assigned one of two states, +1 or −1.…”

Section: Introductionmentioning

confidence: 99%

A Generalized Voter Model on Complex Networks

Schneider-Mizell

Sander

2009

J Stat Phys

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We study a generalization of the voter model on complex networks, focusing on the scaling of mean exit time. Previous work has defined the voter model in terms of an initially chosen node and a randomly chosen neighbor, which makes it difficult to disentangle the effects of the stochastic process itself relative to the network structure. We introduce a process with two steps, one that selects a pair of interacting nodes and one that determines the direction of interaction as a function of the degrees of the two nodes and a parameter α which sets the likelihood of the higher degree node giving its state. Traditional voter model behavior can be recovered within the model. We find that on a complete bipartite network, the traditional voter model is the fastest process. On a random network with power law degree distribution, we observe two regimes. For modest values of α, exit time is dominated by diffusive drift of the system state, but as the high nodes become more influential, the exit time becomes becomes dominated by frustration effects. For certain selection processes and parameters values, an intermediate regime occurs where exit occurs after exponential mixing.

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Voter model dynamics in complex networks: Role of dimensionality, disorder, and degree distribution

Cited by 240 publications

References 45 publications

Social imitation versus strategic choice, or consensus versus cooperation, in the networked Prisoner's Dilemma

Social imitation versus strategic choice, or consensus versus cooperation, in the networked Prisoner's Dilemma

A voter model with time dependent flip rates

A Generalized Voter Model on Complex Networks

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