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Abstract: We study large fluctuations in evolutionary games belonging to thecoordination and anti-coordination classes. The dynamics of these games,modeling cooperation dilemmas, is characterized by a coexistence fixed pointseparating two absorbing states. We are particularly interested in the problemof fixation that refers to the possibility that a few mutants take over theentire population. Here, the fixation phenomenon is induced by largefluctuations and is investigated by a semi-classical WKBWentzel-Kramers-Brillouin theory generalized to treat stochastic systemspossessing multiple absorbing states. Importantly, this method allows us toanalyze the combined influence of selection and random fluctuations on theevolutionary dynamics \textit{beyond} the weak selection limit often consideredin previous works. We accurately compute, including pre-exponential factors,the probability distribution function in the long-lived coexistence state andthe mean fixation time necessary for a few mutants to take over the entirepopulation in anti-coordination games, and also the fixation probability in thecoordination class. Our analytical results compare excellently with extensivenumerical simulations. Furthermore, we demonstrate that our treatment issuperior to the Fokker-Planck approximation when the selection intensity isfinite.



Author: Michael Assaf, Mauro Mobilia

Source: https://arxiv.org/







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