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Cascading Failures and the Robustness of Cooperation in a Unified Scale-Free Network Model

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Complex Networks & Their Applications X (COMPLEX NETWORKS 2021)

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Abstract

In this paper, we examine the effects the cascading failures phenomenon has on unified scale-free complex networks utilizing prisoner’s dilemma game (PDG) dynamics. We find that a single defector may severely impact a large network that may result in a total failure of the entire network. We extend existing results to a network model that unifies the scale-free property and the high-clustering property. Furthermore, we observe that highly connected networks are more vulnerable to the cascading failure effect than less connected ones, as exhibited in both lower average survival rate and lower extinction boundary across different network topologies. As we attempt to examine the cascading failure effect in a more realistic network that is scale-free and highly clustered, we believe that these findings may be beneficial to studying such effects in the real world.

M. Gao and Y. Gao—Equal contribution.

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References

  1. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999). https://doi.org/10.1126/science.286.5439.509

    Article  MathSciNet  MATH  Google Scholar 

  2. Hauert, C., Doebeli, M.: Spatial structure often inhibits the evolution of cooperation in the snowdrift game. Nature 428(6983), 643–646 (2004)

    Article  Google Scholar 

  3. Klemm, K., Eguíluz, V.M.: Growing scale-free networks with small-world behavior. Phys. Rev. E 65(5), 057,102 (2002). https://doi.org/10.1103/PhysRevE.65.057102

  4. Klemm, K., Eguíluz, V.M.: Highly clustered scale-free networks. Phys. Rev. E 65(3), 036,123 (2002)

    Google Scholar 

  5. Kuhn, S.: Prisoner’s Dilemma. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy, Winter, 2019th edn. Stanford University, Metaphysics Research Lab (2019)

    Google Scholar 

  6. Li, M., O’Riordan, C.: The effect of clustering coefficient and node degree on the robustness of cooperation. In: 2013 IEEE Congress on Evolutionary Computation, pp. 2833–2839. IEEE (2013)

    Google Scholar 

  7. Newman, M.E.J., Watts, D.J.: Scaling and percolation in the small-world network model. Phys. Rev. E 60(6), 7332–7342 (1999). https://doi.org/10.1103/PhysRevE.60.7332

    Article  Google Scholar 

  8. Nowak, M.A., May, R.M.: Evolutionary games and spatial chaos. Nature 359(6398), 826–829 (1992)

    Article  Google Scholar 

  9. Ohtsuki, H., Hauert, C., Lieberman, E., Nowak, M.A.: A simple rule for the evolution of cooperation on graphs and social networks. Nature 441(7092), 502–505 (2006)

    Article  Google Scholar 

  10. Roca, C.P., Cuesta, J.A., Sánchez, A.: Evolutionary game theory: temporal and spatial effects beyond replicator dynamics. Phys. Rev. 6(4), 208–249 (2009)

    Google Scholar 

  11. Santos, F.C., Pacheco, J.M.: Scale-free networks provide a unifying framework for the emergence of cooperation. Phys. Rev. Lett. 95(9), 098,104 (2005)

    Google Scholar 

  12. Santos, F.C., Rodrigues, J., Pacheco, J.M.: Graph topology plays a determinant role in the evolution of cooperation. Proc. Royal Soc. B: Biol. Sci. 273(1582), 51–55 (2006)

    Article  Google Scholar 

  13. Szabó, G., Fath, G.: Evolutionary games on graphs. Phys. Rep. 446(4–6), 97–216 (2007)

    Article  MathSciNet  Google Scholar 

  14. Szabó, G., Hauert, C.: Phase transitions and volunteering in spatial public goods games. Phys. Rev. Lett. 89(11), 118,101 (2002)

    Google Scholar 

  15. Szolnoki, A., Perc, M., Danku, Z.: Towards effective payoffs in the Prisoner’s Dilemma game on scale-free networks. Physica A: Stat. Mech. Appl. 387(8–9), 2075–2082 (2008)

    Article  Google Scholar 

  16. Tang, C.L., Wang, W.X., Wu, X., Wang, B.H.: Effects of average degree on cooperation in networked evolutionary game. Eur. Phys. J. B-Condens. Matter Complex Syst. 53(3), 411–415 (2006)

    Article  MATH  Google Scholar 

  17. Wang, W.X., Lai, Y.C., Armbruster, D.: Cascading failures and the emergence of cooperation in evolutionary-game based models of social and economical networks. Chaos 21(3), 033,112 (2011). https://doi.org/10.1063/1.3621719

  18. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998)

    Article  MATH  Google Scholar 

  19. Wu, Z.X., Guan, J.Y., Xu, X.J., Wang, Y.H.: Evolutionary Prisoner’s Dilemma game on Barabási-Albert scale-free networks. Physica A: Stat. Mech. Appl. 379(2), 672–680 (2007)

    Article  Google Scholar 

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Acknowledgements

The authors would like to thank Grinnell College’s Mentored Advanced Projects (MAP program).

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Correspondence to Mingxuan He .

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He, M., Gao, M., Gao, Y., Eliott, F.M. (2022). Cascading Failures and the Robustness of Cooperation in a Unified Scale-Free Network Model. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications X. COMPLEX NETWORKS 2021. Studies in Computational Intelligence, vol 1073. Springer, Cham. https://doi.org/10.1007/978-3-030-93413-2_31

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  • DOI: https://doi.org/10.1007/978-3-030-93413-2_31

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