Please wait a minute...
Chin. Phys. B, 2011, Vol. 20(3): 030203    DOI: 10.1088/1674-1056/20/3/030203
GENERAL Prev   Next  

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
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.

Cite this article: 

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

[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
[1] Evolution of donations on scale-free networks during a COVID-19 breakout
Xian-Jia Wang(王先甲) and Lin-Lin Wang(王琳琳). Chin. Phys. B, 2022, 31(8): 080204.
[2] Social bots and mass media manipulated public opinion through dual opinion climate
Chun Cheng(程纯), Yun Luo(罗云), Chang-bin Yu(于长斌), and Wei-ping Ding(丁卫平). Chin. Phys. B, 2022, 31(1): 018701.
[3] Reputational preference and other-regarding preference based rewarding mechanism promotes cooperation in spatial social dilemmas
Huayan Pei(裴华艳), Guanghui Yan(闫光辉), and Huanmin Wang(王焕民). Chin. Phys. B, 2021, 30(5): 050203.
[4] The impact of honesty and trickery on a Bayesian quantum prisoners' dilemma game
Bo-Yang Liu(刘博阳), Xin Zhao(赵鑫), Hong-Yi Dai(戴宏毅), Ming Zhang(张明), Ying Liao(廖鹰), Xiao-Feng Guo(郭晓峰), Wei Gao(郜伟). Chin. Phys. B, 2020, 29(7): 070201.
[5] The evolution of cooperation in public good game with deposit
Xian-Jia Wang(王先甲), Wen-Man Chen(陈文嫚). Chin. Phys. B, 2019, 28(8): 080201.
[6] Evolutionary game dynamics of combining the Moran and imitation processes
Xian-Jia Wang(王先甲), Cui-Ling Gu(顾翠伶), Shao-Jie Lv(吕少杰), Ji Quan(全吉). Chin. Phys. B, 2019, 28(2): 020203.
[7] Effects of the planarity and heterogeneity of networks on evolutionary two-player games
Xu-Sheng Liu(刘旭升), Zhi-Xi Wu(吴枝喜), Jian-Yue Guan(关剑月). Chin. Phys. B, 2018, 27(12): 120203.
[8] Power control and channel allocation optimization game algorithm with low energy consumption for wireless sensor network
Xiao-Chen Hao(郝晓辰), Jin-Shuo Liu(刘金硕), Li-Xia Xie(解力霞), Bai Chen(陈白), Ning Yao(姚宁). Chin. Phys. B, 2018, 27(8): 080102.
[9] Stochastic evolutionary public goods game with first and second order costly punishments in finite populations
Ji Quan(全吉), Yu-Qing Chu(储育青), Wei Liu(刘伟), Xian-Jia Wang(王先甲), Xiu-Kang Yang(阳修康). Chin. Phys. B, 2018, 27(6): 060203.
[10] On fairness, full cooperation, and quantum game with incomplete information
Zhen-Zhou Lei(雷振州), Bo-Yang Liu(刘博阳), Ying Yi(易英), Hong-Yi Dai(戴宏毅), Ming Zhang(张明). Chin. Phys. B, 2018, 27(3): 030202.
[11] Improving the secrecy rate by turning foes to allies: An auction scheme
Ma Ya-Yan (马亚燕), Wang Bao-Yun (王保云). Chin. Phys. B, 2015, 24(9): 090209.
[12] Spatial snowdrift game in heterogeneous agent systems with co-evolutionary strategies and updating rules
Xia Hai-Jiang (夏海江), Li Ping-Ping (李萍萍), Ke Jian-Hong (柯见洪), Lin Zhen-Quan (林振权). Chin. Phys. B, 2015, 24(4): 040203.
[13] Zero-determinant strategy:An underway revolution in game theory
Hao Dong (郝东), Rong Zhi-Hai (荣智海), Zhou Tao (周涛). Chin. Phys. B, 2014, 23(7): 078905.
[14] Virus spreading in wireless sensor networks with a medium access control mechanism
Wang Ya-Qi (王亚奇), Yang Xiao-Yuan (杨晓元). Chin. Phys. B, 2013, 22(4): 040206.
[15] Hysteresis behavior and nonequilibrium phase transition in a one-dimensional evolutionary game model
Hua Da-Yin (华达银). Chin. Phys. B, 2013, 22(4): 040512.
No Suggested Reading articles found!