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Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042807. Epub 2015 Apr 24.

Analytical description for the critical fixations of evolutionary coordination games on finite complex structured populations.

Zhang L1, Zou Y1,2, Guan S1,2, Liu Z1,2.

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Department of Physics, East China Normal University, Shanghai 200062, China.
State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.


Evolutionary game theory is crucial to capturing the characteristic interaction patterns among selfish individuals. In a population of coordination games of two strategies, one of the central problems is to determine the fixation probability that the system reaches a state of networkwide of only one strategy, and the corresponding expectation times. The deterministic replicator equations predict the critical value of initial density of one strategy, which separates the two absorbing states of the system. However, numerical estimations of this separatrix show large deviations from the theory in finite populations. Here we provide a stochastic treatment of this dynamic process on complex networks of finite sizes as Markov processes, showing the evolutionary time explicitly. We describe analytically the effects of network structures on the intermediate fixations as observed in numerical simulations. Our theoretical predictions are validated by various simulations on both random and scale free networks. Therefore, our stochastic framework can be helpful in dealing with other networked game dynamics.


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