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

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

中国物理B ›› 2011, Vol. 20 ›› Issue (3): 30203-030203.doi: 10.1088/1674-1056/20/3/030203

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

全吉¹, 王先甲²

Institute of Systems Engineering, Wuhan University, Wuhan 430072, China

收稿日期:2010-08-31 修回日期:2010-09-28 出版日期:2011-03-15 发布日期:2011-03-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 71071119) and the Fundamental Research Funds for the Central Universities.

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

Quan Ji(全吉)^a)† and Wang Xian-Jia(王先甲)^a)b)

^a Institute of Systems Engineering, Wuhan University, Wuhan 430072, China; ^b Economics and Management School, Wuhan University, Wuhan 430072, China

Received:2010-08-31 Revised:2010-09-28 Online:2011-03-15 Published:2011-03-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 71071119) and the Fundamental Research Funds for the Central Universities.

摘要/Abstract

摘要： 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 β 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 ε 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.

关键词: evolutionary games, fitness-dependent Moran process, birth--death process, evolutionary stable strategy

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.

Key words: evolutionary games, fitness-dependent Moran process, birth–death process, evolutionary stable strategy

中图分类号: (Decision theory and game theory)

02.50.Le

87.23.Kg (Dynamics of evolution) 05.45.Pq (Numerical simulations of chaotic systems)

全吉, 王先甲. Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation[J]. 中国物理B, 2011, 20(3): 30203-030203.

Quan Ji(全吉) and Wang Xian-Jia(王先甲) . Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation[J]. Chin. Phys. B, 2011, 20(3): 30203-030203.

参考文献 23

[1]	Maynard S J and Price G R 1973 Nature 246 15
[2]	Taylor P D and Jonker L B 1978 Math. Biosci. 40 145
[3]	Maynard S J 1982 Evolution and the Theory of Games (Cambridge: Cambridge University)
[4]	Hofbauer J and Sigmund K 1998 Evolutionary Games and Population Dynamics (Cambridge: Cambridge University)
[5]	Nowak M A and Sigmund K 2004 Science 303 793
[6]	Sigmund K, Hauert C and Nowak M A 2001 Proc. Natl. Acad. Sci. 98 10757
[7]	Hauert C, Holmes M and Doebeli M 2006 Pro. R. Soc. B 273 2565
[8]	Rohl T, Rohl C, Schuster H G and Traulsen A 2007 Phys. Rev. E 76 026114
[9]	Claussen J C and Traulsen A 2008 Phys. Rev. Lett. 100 058104
[10]	Kandori M, Mailath G J and Rob R 1993 Econometrica 61 29
[11]	Amir M and Berninghaus S K 1996 Games Econ. Behav. 14 19
[12]	Moran P A P 1962 The Statistical Processes of Evolutionary Theory (Oxford: Clarendon)
[13]	Taylor C, Fudenberg D, Sasaki A and Nowak M A 2004 Bull. Math. Biol. 66 1621
[14]	Nowak M A, Sasaki A, Taylor C and Fudenberg D 2004 Nature 428 646
[15]	Fudenberg D, Nowak M A, Taylor C and Imhof L A 2006 Theor. Popul. Biol. 70 352
[16]	Traulsen A, Claussen J C and Hauert C 2005 Phys. Rev. Lett. 95 238701
[17]	Traulsen A, Shoresh N and Nowak M A 2008 Bull. Math. Biol. 70 1410
[18]	Traulsen A, Pacheco J M and Imhof L A 2006 Phys. Rev. E 74 021905
[19]	Traulsen A, Nowak M A and Pacheco J M 2006 Phys. Rev. E 74 011909
[20]	Antal T, Nowak M A and Traulsen A 2009 J. Theor. Biol. 257 340
[21]	Antal T, Traulsen A, Ohtsuki H, Tarnita C E and Nowak M A 2009 J. Theor. Biol. 258 614
[22]	Tarnita C E, Antal T and Nowak M A 2009 J. Theor. Biol. 261 50
[23]	Altrock P M and Traulsen A 2009 Phys. Rev. E 80 011909 endfootnotesize

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

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

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