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Chin. Phys. B, 2013, Vol. 22(4): 040512    DOI: 10.1088/1674-1056/22/4/040512
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Hysteresis behavior and nonequilibrium phase transition in a one-dimensional evolutionary game model

Hua Da-Yin (华达银)
Physics Department, Ningbo University, Ningbo 315211, China
Abstract  We investigate a simply evolutionary game model in one dimension. It is found that the system exhibits a discontinuous phase transition from a defection state to a cooperation state when the payoff b of a defector exploiting a cooperator is small. Furthermore, if b is larger enough, the system exhibits two continuous phase transitions between two absorbing states and a coexistence state of cooperation and defection, respectively. The tri-critical point is estimated roughly. Moreover, it is found that the critical behavior of the continuous phase transition with an absorbing state is in the directed percolation universality class.
Keywords:  evolutionary game model      nonequilibrium phase transition with absorbing state      cooperation phenomenon      hysteresis behavior  
Received:  19 July 2012      Revised:  10 September 2012      Accepted manuscript online: 
PACS:  05.70.Ln (Nonequilibrium and irreversible thermodynamics)  
  02.50.Le (Decision theory and game theory)  
  87.23.Ge (Dynamics of social systems)  
  89.75.Hc (Networks and genealogical trees)  
Fund: Project supported by the National Natural Science Foundation of China (Grand No. 10575055) and K. C. Wong Magna Fund in Ningbo University.
Corresponding Authors:  Hua Da-Yin     E-mail:  huadayin@nbu.edu.cn

Cite this article: 

Hua Da-Yin (华达银) Hysteresis behavior and nonequilibrium phase transition in a one-dimensional evolutionary game model 2013 Chin. Phys. B 22 040512

[1] Hammerstein P 2003 Genetic and Cultural Evolution of Cooperation (Cambridge: MIT Press)
[2] Gintis H 2000 Game Theory Evolving (Princeton: Princeton University Press)
[3] Smith J M 1982 Evolution and the Theory of Games (Cambridge: Cambridge University Press)
[4] Nowak M A and Sigmund K 2004 Science 303 793
[5] Szabó G and Fáth G 2007 Phys. Rep. 446 97
[6] Doebeli M, Hauert C and Killingback T 2004 Science 306 859
[7] Nowak M A and May R M 1992 Nature 359 826
[8] Hauert C and Doebeli M 2004 Nature 428 643
[9] Wang X P, Jiang L L and Wang B H 2012 Chin. Phys. B 21 070210
[10] Santos F C and Pacheco J M 2005 Phys. Rev. Lett. 95 098104
[11] Santos F C, Pacheco J M and Lenaerts T 2006 Proc. Natl. Acad. Sci. USA 103 3490
[12] Ohtsuki H, Nowak M A and Pacheco J M 2007 Phys. Rev. Lett. 98 108106
[13] Pacheco J M, Traulsen A and Nowak M A 2006 Phys. Rev. Lett. 97 258103
[14] Antal T, Render S and Sood V 2006 Phys. Rev. Lett. 96 188104
[15] Gómez-Gardeñes J, Campillo M, Floría L M and Moreno Y 2007 Phys. Rev. Lett. 98 108103
[16] Wu Z X and Wang Y H 2007 Phys. Rev. E 75 041114
[17] Wang W X, Ren J, Chen G R and Wang B H 2006 Phys. Rev. E 74 056113
[18] Santos F C, Rodrigues J F and Pacheco J M 2005 Phys. Rev. E 72 056128
[19] Zhong L X, Zheng D F, Zheng B, Xu C and Hui P M 2006 Europhys. Lett. 76 724
[20] Doebeli M, Hauert C and Killingback T 2004 Science 306 859
[21] Wang W X, Lü J H, Chen G R and Hui P M 2008 Phys. Rev. E 77 046109
[22] Vukov J, Szabó G and Szolnoki A 2008 Phys. Rev. E 77 026109
[23] Dickman R and Tomé T 1991 Phys. Rev. A 44 4833
[24] Hinrichsen H 2000 arXiv: cond-mat/0006212
[25] Cardozo G O and Fontanari J F 2006 Eur. Phys. J. B 51 555
[26] Fiore C E and de Oliveira M J 2004 Phys. Rev. E 70 046131
[27] Park S C 2009 Phys. Rev. E 80 061103
[28] Ódor G and Dickman R 2009 J. Stat. Mech.: Theor. Expt. P08024
[29] Fiore C E and de Oliveira M J 2004 Phys. Rev. E 70 046131
[30] Maia D S and Dickman R 2007 J. Phys.: Condens. Matter 19 065143
[31] Chiappin J R N and de Oliveira M J 1999 Phys. Rev. E 59 6419
[32] Bidaux R, Boccara N and Chaté H 1989 Phys. Rev. A 39 3094
[33] Ódor G 2003 Phys. Rev. E 67 016111
[34] Hua D Y, Wang L Y and Chen T 2006 J. Phys. A: Math. Gen. 39 9671
[35] Hua D Y, Weng X Y, Wang L Y and Chen T 2008 Commun. Theor. Phys. 49 960
[36] Ódor G 2004 Rev. Mod. Phys. 76 663
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