Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation

doi:10.1088/1674-1056/20/3/030203

Abstract By using a generalized fitness-dependent Moran process, an evolutionary model for symmetric 2×2 games in a well-mixed population with a finite size is investigated. In the model, the individuals' payoff accumulating from games is mapped into fitness using an exponent function. Both selection strength $\beta$ and mutation rate ε are considered. The process is an ergodic birth-death process. Based on the limit distribution of the process, we give the analysis results for which strategy will be favoured when $\varepsilon$ is small enough. The results depend on not only the payoff matrix of the game, but also on the population size. Especially, we prove that natural selection favours the strategy which is risk-dominant when the population size is large enough. For arbitrary β and ε values, the 'Hawk–Dove' game and the 'Coordinate' game are used to illustrate our model. We give the evolutionary stable strategy (ESS) of the games and compare the results with those of the replicator dynamics in the infinite population. The results are determined by simulation experiments.

Keywords: evolutionary games fitness-dependent Moran process birth–death process evolutionary stable strategy

Received: 31 August 2010
Revised: 28 September 2010
Accepted manuscript online:

PACS:	02.50.Le	(Decision theory and game theory)
	87.23.Kg	(Dynamics of evolution)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 71071119) and the Fundamental Research Funds for the Central Universities.

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Quan Ji(全吉) and Wang Xian-Jia(王先甲) Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation 2011 Chin. Phys. B 20 030203

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Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation

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