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复杂网络的演化博弈是社会结构与稳定的重要模型. 基于单网络演化博弈模型, 提出了一种双复杂动态网络的演化博弈模型, 考虑双复杂网络在两个不同收益矩阵的囚徒困境博弈下增长, 当两个网络没有相互联系时, 发现增长网络中的空间互利性所导致的平均合作水平的突变, 推广了前人的结论. 在两个网络有相互联系时, 平均合作水平可以两者出现高度同步. 在网络的收益系数达到一定时, 才实现较高的合作水平. 增加网络内连接数量时, 自然选择不利于网络的合作, 而公平选择却有利于网络的合作, 说明了更新策略的影响. 当增加网络间连接数量时, 两个网络合作水平都下降. 当保持网络间和网络内的连接比例不变时, 网络的平均度越大, 平均合作水平越小. 本文发现了背叛领袖的存在, 并揭示了双网络模型下背叛领袖对平均合作水平的影响及其与合作领袖的互动机理, 这结果给出社会结构, 稳定和演化的重要信息和启示.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 物理学报 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 物理学报 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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