title: Fixation times in evolutionary games with the Moran and Fermi processes.
abstract: We combined the standard Moran and Fermi process into a mixed process with two strategies C (co-operation) and D (defection). In a well-mixed population of size N+M, N individuals have the same update mechanism as that of Moran process, while the other M individuals have the same update mechanism as that of Fermi process. We obtain the balance equations of the conditional fixation time and unconditional fixation time. What these equations are doing is to make numerical sense for all the figures. We find that the expectation values of conditional fixation times of a single co-operator are smaller than the average values of the standard Moran and Fermi process. In addition, the conditional fixation time of a single co-operator with update rule of Moran is larger than that of Fermi when the intensity of selection is sufficiently small. The simulation results show that the unconditional fixation time of a co-operator who obtains more information is smaller. In addition, the larger the difference of individuals׳ payoff, the smaller the unconditional fixation time.
authors.affiliation: School of Mathematical Science, Dalian University of Technology, Dalian 116024, China.
authors.forename: Xuesong
authors.initials: X
authors.lastname: Liu
authors.affiliation: School of Mathematical Science, Dalian University of Technology, Dalian 116024, China; School of Innovation Experiment, Dalian University of Technology, Dalian 116024, China.
authors.forename: Qiuhui
authors.initials: Q
authors.lastname: Pan
authors.affiliation: School of Mathematical Science, Dalian University of Technology, Dalian 116024, China.
authors.forename: Yibin
authors.initials: Y
authors.lastname: Kang
authors.affiliation: School of Mathematical Science, Dalian University of Technology, Dalian 116024, China.
authors.forename: Mingfeng
authors.initials: M
authors.lastname: He
mesh_terms: D005075:Biological Evolution; D005716:Game Theory; D008954:Models, Biological; D012641:Selection, Genetic; D013997:Time Factors
keywords: Evolution of co-operation; Evolutionary game dynamics; Fixation time; Stochastic dynamics