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On modeling of coevolution of strategies and structure in autonomous overlay networks

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Published:30 July 2012Publication History
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Abstract

Currently, on one hand, there exist much work about network formation and/or growth models, and on the other hand, cooperative strategy evolutions are extensively investigated in biological, economic, and social systems. Generally, overlay networks are heterogeneous, dynamic, and distributed environments managed by multiple administrative authorities, shared by users with different and competing interests, or even autonomously provided by independent and rational users. Thus, the structure of a whole overlay network and the peers' rational strategies are ever coevolving. However, there are very few approaches that theoretically investigate the coevolution between network structure and individual rational behaviors. The main motivation of our article lies in that: Unlike existing work which empirically illustrates the interaction between rational strategies and network structure (through simulations), based on EGT (Evolutionary Game Theory), we not only infer a condition that could favor the cooperative strategy over defect strategy, but also theoretically characterizes the structural properties of the formed network. Specifically, our contributions are twofold. First, we strictly derive the critical benefit-to-cost ratio (b/c) that would facilitate the evolution of cooperation. The critical ratio depends on the network structure (the number of peers in system and the average degree of each peer), and the evolutionary rule (the strategy and linking mutation probabilities). Then, according to the evolutionary rules, we formally derive the structural properties of the formed network in full cooperative state. Especially, the degree distribution is compatible with the power-law, and the exponent is (4-3v)/(1-3v), where v is peer's linking mutation probability. Furthermore, we show that, without being harmful to cooperation evolution, a slight change of the evolutionary rule will evolve the network into a small-world structure (high global efficiency and average clustering coefficient), with the same power-law degree distribution as in the original evolution model.

References

  1. Axelrod, R. 1984. The Evolution of Cooperation. Basic Books.Google ScholarGoogle Scholar
  2. An, B., Vasilakos, A. V., and Lesser, V. 2009. Evolutionary stable resource pricing strategies. In Proceedings of the ACM SIGCOMM Conference on Applications, Technologies, Architectures and Protocols for Computer Communications.Google ScholarGoogle Scholar
  3. Antal, T., Traulsen, A., Ohtsuki, H., Tarnita, C. E., and Nowak, M. A. 2009. Mutation-Selection equilibrium in games with multiple strategies. J. Theor. Biol. 258, 614--622.Google ScholarGoogle ScholarCross RefCross Ref
  4. Boguna, M., Pastor-Satorras, R., Diaz-Guilera, A., and Arenas, A. 2004. Models of social networks based on social distance attachment. Phys. Rev. E70, 056122.Google ScholarGoogle Scholar
  5. Bu, T. and Towsley, D. 2002. On distinguishing between Internet power law topology generators. In Proceedings of the IEEE InfoCom Conference.Google ScholarGoogle Scholar
  6. Clark, D. D., Wroclawski, J., Sollins, K. R., and Braden, R. 2005. Tussle in cyberspace: Defining tomorrow's Internet. IEEE/ACM Trans. Netw. 13, 3. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Cohen, B. 2003. Incentives build robustness in BitTorrent. http://www.bittorrent.com/bittorrentecon.pdfGoogle ScholarGoogle Scholar
  8. Eugster, P. T., Guerraoui, R., Handurukande, S. B., Kermarrec, A. M., and Kouznetsov, P. 2003. Lightweight probabilistic broadcast. ACM Trans. Comput. Syst. 21, 4, 341--374. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Hales, D. 2004. From selfish nodes to cooperative networks: Emergent link-based incentives in peer-to-peer networks. In Proceedings of the 4th IEEE International Conference on Peer-to-Peer Computing (P2P'04). Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Hales, D. and Edmonds, B. 2005. Applying a socially-inspired technique (tags) to improve cooperation in p2p networks. IEEE Trans. Syst. Man Cybernet. A35, 3, 385--395. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Hales, D. and Arteconi, S. 2006. SLACER: A self-organizing protocol for coordination in p2p networks. IEEE Intell. Syst. 21, 2, 29--35. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Holland, J. H. 1993. The effect of labels (tags) on social interactions. Working paper 93-10-064, Santa Fe Institute, Santa Fe, NM.Google ScholarGoogle Scholar
  13. Jelasity, M., Kowalczyk, W., and van Steen, W. 2003. Newscast computing. Tech. rep. IR-CS-006, Vrije Universiteit Amsterdam, Department of Computer Science, Amsterdam, The Netherlands.Google ScholarGoogle Scholar
  14. Jelasity, M., Guerraoui, R., Kermarrec, A. M., and van Steen, W. 2004. The peer sampling service: Experimental evaluation of unstructured gossip-based implementations. In Proceedings of the 5th International Conference on Middleware. Lecture Notes in Computer Science, vol. 3231, Springer. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Jin, E. M., Girvan, M., and Newman, M. E. J. 2001. Structure of growing social networks. Phys. Rev. E64, 4.Google ScholarGoogle Scholar
  16. Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., and Upfal, E. 2000. Stochastic models for the Web graph. In Proceedings of the 41st Annual Symposium on Foundations of Computer Science. 57--65. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Latora, V. and Marchiori, M. 2003. Economic small-world behavior in weighted networks. Euro. Phys. J. B32.Google ScholarGoogle ScholarCross RefCross Ref
  18. Lee, C., Suzuki, J., and Vasilakos, A. V. 2009. iNet-EGT: An evolutionarily stable adaptation framework for network applications. In Proceedings of the BIONETICS Conference.Google ScholarGoogle Scholar
  19. Newman, M. E. J. 2003. The structure and function of complex networks. SIAM Rev. 45, 167--256.Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Nisan, N., Roughgarden, T., Tardos, E., and Vazirani, V. V. 2007. Algorithmic Game Theory. Cambridge University Press. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Nowak, M. A. 2006. Five rules for the evolution of cooperation. Sci. 314.Google ScholarGoogle Scholar
  22. Ohtsuki, H., Bordalo, P., and Nowak, M. A. 2007. The one third law of evolutionary dynamics. J. Theory Biol. 249, 289--295.Google ScholarGoogle ScholarCross RefCross Ref
  23. Ohtsuki, H. and Nowak, M. A. 2006. The replicator equation on graphs. J. Theor. Biol. 243, 86--97.Google ScholarGoogle ScholarCross RefCross Ref
  24. Onnela, J. P., Saramaki, J., Hyvonen, J., Szabo, G., Lazer, D., Kaski, K., Kertesz, J., and Barabasi, A.-L. 2007. Structure and tie strengths in mobile communication networks. Proc. Nat. Acad. Sci. 104.Google ScholarGoogle Scholar
  25. Pacheco, J. M., Traulsen, A., and Nowak, M. A. 2006. Active linking in evolutionary games. J. Theor. Biol. 243, 437--443.Google ScholarGoogle ScholarCross RefCross Ref
  26. Qiu, D. Y. and Srikant, R. 2004. Modeling and performance analysis of BitTorrent-like peer-to-peer networks. In Proceedings of the ACM SIGCOMM Conference on Applications, Technologies, Architectures and Protocols for Computer Communications. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Roca, C. P., Cuesta, J. A., and Sanchez, A. 2009. Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics. Phys. Life Rev. 6, 4, 208--249.Google ScholarGoogle ScholarCross RefCross Ref
  28. Santos, F. C., Santos, M. D., and Pacheco, J. M. 2008. Social diversity promotes the emergence of cooperation in public goods games. Nature 454.Google ScholarGoogle Scholar
  29. Tarnita, C. E., Antal, T.. Ohtsuki, H., and Nowak, M. A. 2009. Evolutionary dynamics in set structured populations. Proc. Nat. Acad. Sci. 106, 8601--8604.Google ScholarGoogle ScholarCross RefCross Ref
  30. Traulsen, A. and Schuster, H. G. 2003. Minimal model for tag-based cooperation. Phys. Rev. E68, 4.Google ScholarGoogle Scholar
  31. Traulsen, A., Nowak, M. A., and Pacheco, J. M. 2006. Stochastic dynamics of invasion and fixation. Phys. Rev. E74.Google ScholarGoogle Scholar
  32. Traulsen, A. and Nowak, M. A. 2006. Evolution of cooperation by multilevel selection. Proc. Nat. Acad. Sci. 103, 29.Google ScholarGoogle ScholarCross RefCross Ref
  33. Traulsen, A. and Nowak, M. A. 2007. Chromodynamics of cooperation in finite populations. PLoS One 2, 3.Google ScholarGoogle ScholarCross RefCross Ref
  34. Traulsen, A. and Hauert, C. 2009. Stochastic evolutionary game dynamics. In Reviews of Nonlinear Dynamics and Complexity, vol. 2, H. G. Schuster, Ed., Wiley-VCH.Google ScholarGoogle Scholar
  35. Traulsen, A., Shoresh, N., and Nowak, M. A. 2008. Analytical results for individual and group selection of any intensity. B Math. Biol. 70, 1410--1424.Google ScholarGoogle ScholarCross RefCross Ref
  36. Wang, Y. F. and Nakao, A. 2008. Research issues and overview of incentive-compatible topology evolution in autonomous overlay networks. In Proceedings of the 3rd ChinaGrid Conference. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. Wang, Y. F. and Nakao, A. 2010. On cooperative and efficient overlay network evolution based on group selection pattern. IEEE Trans. Syst. Man Cybernet. B40, 3. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Watts, D. J. and Strogatz, S. H. 1998. Collective dynamics of ‘small-world’ networks. Nature 393.Google ScholarGoogle Scholar

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      • Published in

        cover image ACM Transactions on Autonomous and Adaptive Systems
        ACM Transactions on Autonomous and Adaptive Systems  Volume 7, Issue 2
        July 2012
        275 pages
        ISSN:1556-4665
        EISSN:1556-4703
        DOI:10.1145/2240166
        Issue’s Table of Contents

        Copyright © 2012 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 30 July 2012
        • Accepted: 1 March 2011
        • Revised: 1 December 2010
        • Received: 1 June 2010
        Published in taas Volume 7, Issue 2

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