Abstract
Community structure is one of the most ubiquitous and important features of many real systems, such as social, economy and biology networks. In this paper, we study the evolutionary dynamics in the realm of a generalized prisoner’s dilemma game on network which exhibits community structure and power law degree distribution co-evolving with the strategies. In our game, each person can be a cooperator, a defector or a super cooperator. A super cooperator is a cooperator who trusts other people much more than the normal one. During the evolution, when the expectation payoff is below a certain value, a link between the player and one of its neighbors will be broken and rewired to a cooperator or a super cooperator on network. Our results point out that lower trust degree can break the community structure of the network and inhibit the emergence of cooperation.
Similar content being viewed by others
References
Maynard-Smith, J., & Szathmary, E. (1995). The major transitions in evolution. Nature, 374(6519), 227–232.
Nowak, M. A. (2004). Prisoners of the dilemma—When mathematics and biology met on a mountain. Nature, 427(6974), 491.
Hauert, C., & Szabó, G. (2005). Game theory and physics. American Journal of Physics, 73, 405.
Nowak, M. A. (2006). Five rules for the evolution of cooperation. Science, 314, 1560–1563.
Ohtsuk, H., Hauert, C., Lieberman, E., & Nowak, M. A. (2006). A simple rule for the evolution of cooperation on graphs and social networks. Nature, 441, 502–505.
Gómez-Gardenẽs, J., Campillo, M., Floría, L., & Moreno, Y. (2007). Dynamical organization of cooperation in complex topologies. Physical Review Letters, 98(10), 108103.
Roca, C. P., Cuesta, J. A., & Sánchez, A. (2009). Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics. Physics of Life Reviews, 6(4), 208–249.
Kim, B. J., Trusina, A., Holme, P., Minnhagen, P., Chung, J. S., & Choi, M. Y. (2002). Dynamic instabilities induced by asymmetric influence: Prisoners’ dilemma game in small-world networks. Physical Review E, 66(2), 021907.
Tomassini, M., Luthi, L., & Giacobini, M. (2006). Hawks and Doves on small-world networks. Physical Review E, 73(1), 016132.
Rong, Z., Yang, H.-X., & Wang, W.-X. (2010). Feedback reciprocity mechanism promotes the cooperation of highly clustered scale-free networks. Physical Review E, 82(4), 047101.
Tang, C.-L., Wang, W.-X., Wu, X., & Wang, B.-H. (2006). Effects of average degree on cooperation in networked evolutionary game. The European Physical Journal B-Condensed Matter and Complex Systems, 53(3), 411–415.
Santos, F. C., & Pacheco, J. M. (2005). Scale-free networks provides a unifying framework for the emergence of cooperation. Physical Review Letters, 95(9), 098104.
Santos, F. C., Santos, M. D., & Pacheco, J. M. (2008). Social diversity promotes the emergence of cooperation in public good games. Nature, 454(7201), 213–216.
Wu, Z.-X., Rong, Z.-H., & Yang, H.-X. (2015). Impact of heterogeneous activity and community structure on the evolutionary success of cooperator in social networks. Physical Review E, 91(1), 012802.
Wu, J.-S., Hou, Y.-Q., Jiao, L.-C., & Li, H.-J. (2014). Community structure inhibits cooperation in the spatial prisoner’s dilemma. Physica A, 412, 169–179.
Lozano, S., Arenas, A., & Sánchez, A. (2008). Mesoscopic structure conditions the emergence of cooperation on social networks. PLoS ONE, 3(4), e1892.
Zimmermann, M. G., Eguíluz, V. M., & San, M. M. (2004). Coevolution of dynamical states and interactions in dynamic networks. Physical Review E, 69(6), 065102.
Ren, J., Wu, X., Wang, W.-X., Chen, G., & Wang. B.-H. (2006). Interplay between evolutionary game and network structure: The coevolution of social net, cooperation and wealth. arXiv preprint physics 0605250.
Fu, F., Hauert, C., Nowak, M.-A., & Wang, L. (2008). Reputation-based partner choice promotes cooperation in social networks. Physical Review E, 78(2), 026117.
Eisert, J., Wilkens, M., & Lewenstein, M. (1999). Quantum games and quantum strategies. Physical Review Letters, 83, 3077–3080.
Li, Q., Chen, M., Perc, M., Iqbal, A., & Abbott, D. (2013). Effects of adaptive degrees of trust on coevolution of quantum strategies on scale-free networks. Scientific Reports, 3, 2949.
Li, Q., Iqbal, A., Chen, M., & Abbott, D. (2012). Evolution of quantum and classical strategies on networks by group interactions. New Journal of Physics, 14(10), 103034.
Li, A., & Yong, X. (2014). Entanglement guarantees emergence of cooperation in quantum prisoner’s dilemma games on networks. Scientific Reports, 4, 6286.
Li, A., & Yong, X. (2015). Emergence of super cooperation of prisoner’s dilemma games on scale-free networks. PLoS ONE, 10(2), e0116429.
Palla, G., Derényi, I., Farkas, I., & Vicsek, T. (2005). Uncovering the overlapping community structure of complex networks in nature and society. Nature, 435(7043), 814–818.
Palla, G. L., Barabási, A., & Vicsek, T. (2007). Quantifying social group evolution. Nature, 446(7136), 664–667.
Ahn, Y. Y., Bagrow, J. P., & Lehmann, S. (2010). Link communities reveal multiscale complexity in networks. Nature, 466(7307), 761–764.
Faccin, M., Migdał, P., Johnson, T. H., Bergholm, V., & Biamonte, J. D. (2014). Community detection in quantum complex networks. Physical Review X, 4(4), 041012.
Lancichinetti, A., Fortunato, S., & Radicchi, F. (2008). Benchmark graphs for testing community detection algorithms. Physical Review E, 78(4), 046110.
Wu, Z.-X., Xu, X.-J., Huang, Z.-G., Wang, S.-J., & Yang, Y.-H. (2006). Evolutionary prisoner’s dilemma game with dynamic preferential selection. Physical Review E, 74, 021107.
Szabó, G., & Tőke, C. (1998). Evolutionary prisoner’s dilemma game on a square lattice. Physical Review E, 58(1), 69.
Vukov, J., Szabó, G., & Szolnoki, A. (2008). Evolutionary prisoner’s dilemma game on Newman–Watts networks. Physical Review E, 77, 026109.
Newman, M. E., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69(2), 026113.
Rosvall, M., & Bergstrom, T. (2008). Maps of random walks on complex networks reveal community structure. Proceedings of the National Academy of Sciences, 105(4), 1118–1123.
Bavelas, A. (1950). Communication patterns in task-oriented groups. The Journal of the Acoustical Society of America, 22(6), 725–730.
Beauchamp, M. A. (1965). An improved index of centrality. Behavioral Science, 10(2), 161–163.
Acknowledgements
This research was supported by the MOA monitoring statistics Project on Agricultural and rural resources founded by Ministry of Agriculture PRC, the MOA Innovative Talents Project founded by the Ministry of Agriculture PRC, the Science and Technology Innovation Project Fund of Chinese Academy of Agricultural Sciences (CAAS - ASTIP- 2017 – AI I- 01).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhuang, J., Yong, X., Zhao, J. et al. Trust Degree can Preserve Community Structure on Co-evolving Complex Networks in Spatial Generalized Prisoner’s Dilemma Game. Wireless Pers Commun 102, 3089–3100 (2018). https://doi.org/10.1007/s11277-018-5328-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11277-018-5328-y