摘要We introduce a simple model based on the Moran process with network dynamics. Using pair approximation, the cooperation frequencies at equilibrium states are deduced for general interactions. Three usual social dilemmas are discussed in the framework of our model. It is found that they all have a phase transition at the same value of cost-to-benefit ratio. For the prisoner's dilemma game, notably it is exactly the simple rule reported in the literature [Nature 441(2006)502]. In our model, the simple rule results from the parent-offspring link. Thus the basic mechanism for cooperation enhancement in network reciprocity is in line with the Hamilton rule of kin selection. Our simulations verify the analysis obtained from pair approximation.
Abstract：We introduce a simple model based on the Moran process with network dynamics. Using pair approximation, the cooperation frequencies at equilibrium states are deduced for general interactions. Three usual social dilemmas are discussed in the framework of our model. It is found that they all have a phase transition at the same value of cost-to-benefit ratio. For the prisoner's dilemma game, notably it is exactly the simple rule reported in the literature [Nature 441(2006)502]. In our model, the simple rule results from the parent-offspring link. Thus the basic mechanism for cooperation enhancement in network reciprocity is in line with the Hamilton rule of kin selection. Our simulations verify the analysis obtained from pair approximation.
YANG Dong-Ping;LIN Hai;WU Chen-Xu;SHUAI Jian-Wei. Modelling Moran Process with Network Dynamics for the Evolution of Cooperation[J]. 中国物理快报, 2009, 26(6): 68902-068902.
YANG Dong-Ping, LIN Hai, WU Chen-Xu, SHUAI Jian-Wei. Modelling Moran Process with Network Dynamics for the Evolution of Cooperation. Chin. Phys. Lett., 2009, 26(6): 68902-068902.
[1] Taylor C and Nowak M A 2007 Evolution 61 2281 [2] Nowak M A 2006 Evolutionary Dynamics: Exploring theEquations of Life (Cambridge: Harvard University) [3] Nowak M A 2006 Science 314 1560 [4] Traulsen A, Claussen J C and Hauert C 2005 Phys. Rev.Lett. 95 238701 [5] Smith J M 1982 Evolution and the Theory of Games(Cambridge: Cambridge University) [6] Hofbauer J and Sigmund K 1998 Evolutionary Games andPopulation Dynamics (Cambridge: Cambridge University) [7] Nowak M A, Sasaki A, Taylor C and Fudenberg D 2004 Nature 428 646 [8] Moran P A P 1962 The Statistical Processes ofEvolutionary Theory (Oxford: Clarendon) [9] Hamilton W D 1964 J. Theor. Biol. 7 1 [10] Axelrod R and Hamilton W 1981 Science 2111390 [11] Nowak M A and Sigmund K 1998 Nature 393 573 [12] Traulsen A, Nowak M A 2006 Proc. Natl. Acad. Sci.USA 103 10952 [13] Nowak M A and May R M 1992 Nature 359 826 [14] Chen Y S, Lin H and Wu C X 2007 Physica A 385379 [15] Assenza S, G\'{omez-Garde\~{nes J and Latora V 2008 Phys. Rev. E 78 017101 [16] Hauert C and Doebeli M 2004 Nature 428 643 [17] Santos F C and Pacheco J M 2005 Phys. Rev. Lett. 95 098104. [18] Santos F C, Pacheco J M and Lenaerts T 2006 Proc.Natl. Acad. Sci. U.S.A. 103 3490 [19] Santos F C, Rodrigues J F and Pacheco J M 2006 Proc.R. Soc. London B 273 51 [20] Santos F C and Pacheco J M 2006 J. Evol. Biol. 19 726 [21] Ohtsuki H, Hauert C, Lieberman E and Nowak M A 2006 Nature 441 502 [22] Hatzopoulos V and Jensen H J 2008 Phys. Rev. E 78 011904 [23] Hauert C and Szab\'{o G 2005 Am. J. Phys. 73405 [24] Szab\'{o G and F\'{ath G 2007 Phys. Rep. 446 97 [25] Wu Z X and Wang Y H 2007 Phys. Rev. E 75041114 [26] Wang W X, Ren J, Chen G, and Wang B H 2006 Phys.Rev. E 74 056113 [27] Wang W X, L\"{u J H, Chen G R and Hui P M 2008 Phys. Rev. E 77 046109 [28] Zhang M F et al 2008 Chin. Phys. Lett. 251494 [29] Zhong L X, Qiu T and Xu J R 2008 Chin. Phys. Lett. 25 2315 [30] Ficici S and Pollack J 2007 J. Theor. Biol. 247 426
2009, Vol. 26 
