Fixation times in evolutionary games with the Moran and Fermi processes

• A Moran and Fermi mixed process is proposed.
• The conditional fixation time of a co-operator with Moran rule is larger than that of Fermi.
• The unconditional fixation time of a co-operator who obtains more information is smaller.
• The larger the difference of individuals׳ payoff, the smaller the unconditional fixation time.

We combined the standard Moran and Fermi process into a mixed process with two strategies CC (co-operation) and DD (defection). In a well-mixed population of size N+MN+M, NN individuals have the same update mechanism as that of Moran process, while the other MM 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.