Anomalous Metastability and Fixation Properties of Evolutionary Games on Scale-Free Graphs

Assaf, Michael; Mobilia, Mauro

doi:10.1007/978-3-319-00395-5_88

Cited by 1 publication

(14 citation statements)

References 38 publications

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“…2), considering ω to be constant instead of ρ leads to a large error in the MFT. Here, by carrying out extensive simulations on large systems (up to two orders of magnitude larger than in [66,67]), and by correcting our theoretical analysis, we have confirmed that the fixation properties of ACGs evolving with the LD exhibit a linear dependence on N which, as seen above, is consistent with the (approximate) conservation of ρ by the LD under weak selection (see Fig. 2).…”

Section: Fixation Propertiessupporting

confidence: 79%

“…Therefore, the fixation probability and MFT of the ACGs with the LD are not affected by the scale-free topology, contrary to what was reported in Ref. [66,67]. Yet, a completely different scenario emerges with the VM update rule, where the scale-free topology strongly affects the long-time behavior.…”

Section: A Timescale Separation and Effective Diffusion Theory For Thecontrasting

confidence: 60%

“…[66,67], φ C and the MFT of ACGs evolving with the LD are not affected by the scale-free topology. Therefore, in ACGs with the LD, T fix always grows exponentially withsN (within error bars) as illustrated in Fig.…”

Section: Fixation Propertiesmentioning

confidence: 93%

“…Various types of update rules are possible and, in the case of models without fitness-dependent selection, it has been found that the dynamics may depend crucially on the details of the underlying rules [46][47][48][49][50][51][52][53]. Here, we consider two important choices: the so called (i) "voter model" (VM) rule [48][49][50]; (ii) and the "link dynamics" (LD) [46,47,66,67]: (i) In the VM dynamics, a focal agent i is chosen at random with probability 1/N , and then one of its neighbors is picked with a probability 1/k i . In this death-first/birth-second process, the focal agent dies and is replaced by the picked neighbor with a probability proportional to the fitness of the latter.…”

Section: B Spatially-structured Settingmentioning

confidence: 99%

“…Here, we first examine the case of the VM update, and then critically revisit the case of the LD discussed in Refs. [66,67]. ' Here, we illustrate the dynamics of different density quantities in the system: the total density of the cooperators, ρ, the subgraph densities of the cooperators of degree 2 and 7, ρ 2 and ρ 7 , and the degree-weighted density of cooperators, ω, calculated by summing up to degree k = 200.…”

Section: Timescale Separation and Effective Diffusion Approximationmentioning

confidence: 99%

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Large fluctuations in anti-coordination games on scale-free graphs

Sabsovich¹,

Mobilia²,

Assaf³

2017

J. Stat. Mech.

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We study the influence of the complex topology of scale-free graphs on the dynamics of anti-coordination games (e.g. snowdrift games). These reference models are characterized by the coexistence (evolutionary stable mixed strategy) of two competing species, say "cooperators" and "defectors", and, in finite systems, by metastability and large-fluctuation-driven fixation. In this work, we use extensive computer simulations and an effective diffusion approximation (in the weak selection limit) to determine under which circumstances, depending on the individual-based update rules, the topology drastically affects the long-time behavior of anti-coordination games. In particular, we compute the variance of the number of cooperators in the metastable state and the mean fixation time when the dynamics is implemented according to the voter model (death-first/birth-second process) and the link dynamics (birth/death or death/birth at random). For the voter update rule, we show that the scale-free topology effectively renormalizes the population size and as a result the statistics of observables depend on the network's degree distribution. In contrast, such a renormalization does not occur with the link dynamics update rule and we recover the same behavior as on complete graphs.

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Section: Fixation Propertiessupporting

confidence: 79%

Section: A Timescale Separation and Effective Diffusion Theory For Thecontrasting

confidence: 60%

Section: Fixation Propertiesmentioning

confidence: 93%