Research article Special Issues

The role of self-loops and link removal in evolutionary games on networks

  • Received: 28 December 2018 Accepted: 09 April 2019 Published: 11 June 2019
  • Recently, a new mathematical formulation of evolutionary game dynamics [1] has been introduced accounting for a finite number of players organized over a network, where the players are located at the nodes of a graph and edges represent connections between them. Internal steady states are particularly interesting in control and consensus problems, especially in a networked context where they are related to the coexistence of different strategies. In this paper we consider this model including self-loops. Existence of internal steady states is studied for different graph topologies in two-strategy games. Results on the effect of removing links from central players are also presented.

    Citation: Dario Madeo, Chiara Mocenni, Jean Carlo Moraes, Jorge P. Zubelli. The role of self-loops and link removal in evolutionary games on networks[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 5287-5306. doi: 10.3934/mbe.2019264

    Related Papers:

  • Recently, a new mathematical formulation of evolutionary game dynamics [1] has been introduced accounting for a finite number of players organized over a network, where the players are located at the nodes of a graph and edges represent connections between them. Internal steady states are particularly interesting in control and consensus problems, especially in a networked context where they are related to the coexistence of different strategies. In this paper we consider this model including self-loops. Existence of internal steady states is studied for different graph topologies in two-strategy games. Results on the effect of removing links from central players are also presented.


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    [1] D. Madeo and C. Mocenni, Game Interactions and dynamics on networked populations, IEEE T. Automat. Contr., 60 (2015), 1801–1810.
    [2] A. Barrat, M. Barthelemy and A. Vespignani, Dynamical Processes on Complex Networks. Cambridge University Press, UK, 2008.
    [3] G. Ehrhardt, M. Marsili and F. Vega-Redondo, Diffusion and growth in an evolving network, Int. J. Game Theory, 334 (2006), 383–397.
    [4] V. Colizza, A. Barrat, M. Barthélemy, et al., The role of the airline transportation network in the prediction and predictability of global epidemics, P. Natl. Acad. Sci. USA, 103 (2006), 2015–2020.
    [5] V. Colizza and A. Vespignani, Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: Theory and simulations, J. Theor. Biol., 251 (2008), 450–467.
    [6] S. Tully, M. G. Cojocaru and C. T. Bauch, Multiplayer games and HIV transmission via casual encounters, Math. Biosci. Eng., 14 (2017), 359–376.
    [7] M. D'Orsogna and M. Perc, Statistical physics of crime: A review, Phys. Life Rev., 12 (2015), 1–21.
    [8] D. Madeo, L. R. Comolli and C. Mocenni, Emergence of microbial networks as response to hostile environments, Front. Microbiol., 5 (2014), 407.
    [9] N. Quijano, C. Ocampo-Martinez, J. Barreiro-Gomez, et al., The role of population games and evolutionary dynamics in distributed control systems: The advantages of evolutionary game theory, IEEE Contr. Sys. Mag., 37 (2017), 70–97.
    [10] R. Gray, A. Franci, V. Srivastava, et al., Multi-agent decision-making dynamics inspired by honeybees, IEEE T. Contr. Netw. Sys., 5 (2018), 793–806.
    [11] F. C. Santos, J. M. Pacheco and T. Lenaerts, Evolutionary dynamics of social dilemmas in structured heterogeneous populations, P. Natl. Acad. Sci. USA, 103 (2006), 3490–3494.
    [12] H. Ohtsuki and M. A. Nowak, The replicator equation on graphs, J. Theor. Biol., 243 (2006), 86–97.
    [13] T. Konno, A condition for cooperation in a game on complex networks, J. Theor. Biol., 269 (2011), 224–233.
    [14] J. Gómez-Gardenes, I. Reinares, A. Arenas, et al., Evolution of cooperation in multiplex networks, Sci. Rep., 2 (2012), 620.
    [15] S. M. Cameron and A. Cintrón-Arias, Prisoner's Dilemma on real social networks: Revisited, Math. Biosci. Eng., 10 (2013), 1381–1398.
    [16] D. G. Rand, M. A. Nowak, J. H. Fowler, et al., Static network structure can stabilize human cooperation, P. Natl. Acad. Sci. USA, 11 (2014), 17093–17098.
    [17] B. Allen, G. Lippner, Y. Chen, et al., Evolutionary dynamics on any population structure, Nature, 544 (2017), 227.
    [18] B. Fotouhi, N. Momeni, B. Allen, et al., Evolution of Cooperation on Stochastic Block Models, preprint, arXiv:1807.03093.
    [19] J. Weibull, Evolutionary Game Theory, MIT Press, Cambridge, MA, 1995.
    [20] J. Hofbauer and K. Sigmund, Evolutionary game dynamics, B. Am. Math. Soc, 40 (2003) 479–519.
    [21] M. A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life, Belknap Press of Harvard University Press, Harvard, MA, 2006.
    [22] G. Iacobelli, D. Madeo and C. Mocenni, Lumping evolutionary game dynamics on networks, J. Theor. Biol., 407 (2016), 328–338.
    [23] D. Pais, C. H. Caicedo-Nùñez and N. E. Leonard, Hopf bifurcations and limit cycles in evolutionary network dynamics, SIAM J. Appl. Dyn. Syst., 11 (2012), 1754–1884.
    [24] W. Ren and R. Beard, Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE T. Automat. Contr., 50 (2005), 655–661.
    [25] R. Olfati-Saber, A. Fax and R. Murray, Consensus and cooperation in networked multi-agent systems, P. IEEE, 95 (2007), 215–233.
    [26] B. Kozma and A. Barrat, Consensus formation on adaptive networks, Phys. Rev. E, 77 (2008), 016102.
    [27] G. Punzo, G. F. Young, M Macdonald, et al., Using network dynamical influence to drive consensus, Sci. Rep., 6 (2016), 26318.
    [28] A. Traulsen, F. C. Santos and J. M. Pacheco, Evolutionary Games in Self-Organizing Populations, in Adaptive networks: Theory, Models and Applications (eds. T. Gross and H. Sayama), Springer Berlin Heidelberg, Germany, (2009), 253–267.
    [29] S. Boccaletti, V. Latora, Y. Moreno, et al., Complex networks: Structure and dynamics, Phys. Rep., 424 (2006), 175–308.
    [30] Y. Bramoullé and R. Kranton, Games Played on Networks, in The Oxford Handbook of the Economics of Networks (eds. Y. Bramoullé, A. Galeotti and B. Rogers), Oxford University Press. Available from: http://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199948277.001. 0001/oxfordhb-9780199948277.
    [31] A. Banerjee, A. G. Chandrasekhar, E. Duflo, et al., Gossip: Identifying Central Individuals in a Social Network, preprint, arXiv:1406.2293v3.
    [32] D. Madeo and C. Mocenni, Self-regulation promotes cooperation in social networks, preprint, arXiv:1807.07848.
    [33] M. Newman, Network: An introduction, Oxford University Press, 2010.
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