TY - JOUR
T1 - Large fluctuations in anti-coordination games on scale-free graphs
AU - Sabsovich, Daniel
AU - Mobilia, Mauro
AU - Assaf, Michael
N1 - Publisher Copyright:
© 2017 IOP Publishing Ltd and SISSA Medialab srl.
PY - 2017/5/22
Y1 - 2017/5/22
N2 - 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.
AB - 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.
KW - evolutionary game theory
KW - large deviation
KW - networks
KW - random graphs
KW - stochastic processes
UR - http://www.scopus.com/inward/record.url?scp=85020043163&partnerID=8YFLogxK
U2 - 10.1088/1742-5468/aa6a21
DO - 10.1088/1742-5468/aa6a21
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AN - SCOPUS:85020043163
SN - 1742-5468
VL - 2017
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
IS - 5
M1 - 053405
ER -