Sabsovich, D, Mobilia, M orcid.org/0000-0002-1424-567X and Assaf, M (2017) Large Fluctuations in Anti-Coordination Games on Scale-Free Graphs. Journal of Statistical Mechanics: Theory and Experiment. 053405. ISSN 1742-5468
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 IOP Publishing Ltd and SISSA Medialab srl. This is an author-created, un-copyedited version of an article published in Journal of Statistical Mechanics: Theory and Experiment . IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1742-5468/aa6a21. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | evolutionary game theory, large deviation, stochastic processes, random graphs, networks |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 May 2017 11:41 |
Last Modified: | 22 May 2018 00:38 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1742-5468/aa6a21 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:116651 |