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The dynamic complex network is an important model of social structure and stability. Based on the single dynamic complex network, we propose a growing double-network evolutionary gambling model. When the two networks are separated, we find that the average of cooperation strategy has a jump as the payoff increases, which can be regarded as a phase transition. This result is a generalized result of static gambling network. When the two networks are connected, their averages of cooperation strategy are synchronized. When the intra-linkages are increased, the natural selection does not favor cooperation, while the fair selection does. When the inter-linkages are increased, the average of cooperation strategy decreases for both networks. As the ratio of inter- and intra- linkage is constant, the more the average degree, the less the cooperation. We find the existence of defection leader, and uncover its influence on the average of cooperation strategy and how it interacts with cooperation leader. These results provide some hints to understand the social structure, stability and evolution.
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Keywords:
- two networks /
- different payoff matrices /
- evolutionary games
[1] Satoru M, Jin Y 2013 Phys. Rev. E 88 052809
[2] Cui A X, Fu Y, Shang M S, Chen D B, Zhou T 2011 Acta Phys. Sin. 60 038901 (in Chinese) [崔爱香, 傅彦, 尚明生, 陈端兵, 周涛 2011 60 038901]
[3] Maslov S, Sneppen K, Zaliznyak A 2004 Physica A 333 529
[4] Jin-Li G 2010 Chin. Phys. B 19 120503
[5] Casasnovas J P 2012 Ph. D. Dissertation (Zaragoza, Spain: University of Zaragoza)
[6] Wu Z X, Guan J Y, Xu X J, Wang Y H 2007 Physica A 379 672
[7] Tomassini M, Luthi L, Giacobini M 2006 Phys. Rev. E 73 016132
[8] Nowak M A 2006 Science 314 1560
[9] Wang Z, Szolnoki A, Perc M 2013 Scientific Report 3 1183
[10] Wang Z, Kokubo S, Tanimoto J, Fukuda E, Shigaki K 2013 Phys. Rev. E 88 042145
[11] Chen X, Fu F, Wang L 2007 Physica A 378 512
[12] Guan J Y, Zhi-Xi W, Zi-Gang H, Ying-Hai Wa 2010 Chin. Phys. B 19 020203
[13] Floría L, M, Gracia-Lázaro C, Gómez-Gardeñes J, Moreno Y 2009 Phys. Rev. E 79 026106
[14] Ichinose G, Tenguishi Y 2013 Phys. Rev. E 88 052808
[15] Wu, B, Altrock P M, Wang L, Traulsen A 2010 Phys. Rev. E 82 046106
[16] Portillo I G 2012 Eur. Phys. J. B 85 409
[17] Santos F C, Pacheco J M 2005 Phys. Rev. Lett. 95 098104
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[1] Satoru M, Jin Y 2013 Phys. Rev. E 88 052809
[2] Cui A X, Fu Y, Shang M S, Chen D B, Zhou T 2011 Acta Phys. Sin. 60 038901 (in Chinese) [崔爱香, 傅彦, 尚明生, 陈端兵, 周涛 2011 60 038901]
[3] Maslov S, Sneppen K, Zaliznyak A 2004 Physica A 333 529
[4] Jin-Li G 2010 Chin. Phys. B 19 120503
[5] Casasnovas J P 2012 Ph. D. Dissertation (Zaragoza, Spain: University of Zaragoza)
[6] Wu Z X, Guan J Y, Xu X J, Wang Y H 2007 Physica A 379 672
[7] Tomassini M, Luthi L, Giacobini M 2006 Phys. Rev. E 73 016132
[8] Nowak M A 2006 Science 314 1560
[9] Wang Z, Szolnoki A, Perc M 2013 Scientific Report 3 1183
[10] Wang Z, Kokubo S, Tanimoto J, Fukuda E, Shigaki K 2013 Phys. Rev. E 88 042145
[11] Chen X, Fu F, Wang L 2007 Physica A 378 512
[12] Guan J Y, Zhi-Xi W, Zi-Gang H, Ying-Hai Wa 2010 Chin. Phys. B 19 020203
[13] Floría L, M, Gracia-Lázaro C, Gómez-Gardeñes J, Moreno Y 2009 Phys. Rev. E 79 026106
[14] Ichinose G, Tenguishi Y 2013 Phys. Rev. E 88 052808
[15] Wu, B, Altrock P M, Wang L, Traulsen A 2010 Phys. Rev. E 82 046106
[16] Portillo I G 2012 Eur. Phys. J. B 85 409
[17] Santos F C, Pacheco J M 2005 Phys. Rev. Lett. 95 098104
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