Letter | Published:

Successful strategies for competing networks

Nature Physics volume 9, pages 230234 (2013) | Download Citation

Abstract

Competitive interactions represent one of the driving forces behind evolution and natural selection in biological and sociological systems1,2. For example, animals in an ecosystem may vie for food or mates; in a market economy, firms may compete over the same group of customers; sensory stimuli may compete for limited neural resources to enter the focus of attention. Here, we derive rules based on the spectral properties of the network governing the competitive interactions between groups of agents organized in networks. In the scenario studied here the winner of the competition, and the time needed to prevail, essentially depend on the way a given network connects to its competitors and on its internal structure. Our results allow assessment of the extent to which real networks optimize the outcome of their interaction, but also provide strategies through which competing networks can improve on their situation. The proposed approach is applicable to a wide range of systems that can be modelled as networks3.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life (John Murray, 1869).

  2. 2.

    An Inquiry into the Nature and Causes of the Wealth of Nations (W. Strahan & T. Cadell, 1776).

  3. 3.

    , , , & Complex networks: Structure and dynamics. Phys. Rep. 424, 175–308 (2006).

  4. 4.

    , , & Network robustness and fragility: Percolation on random graphs. Phys. Rev. Lett. 85, 5468–5471 (2000).

  5. 5.

    , , & Resilience of the internet to random breakdowns. Phys. Rev. Lett. 85, 4626–4628 (2000).

  6. 6.

    , , , & Synchronization in complex networks. Phys. Rep. 469, 93–153 (2008).

  7. 7.

    & Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86, 3200–3203 (2001).

  8. 8.

    & Information transfer and phase transitions in a model of internet traffic. Physica A 289, 595–605 (2001).

  9. 9.

    , & Communication in networks with hierarchical branching. Phys. Rev. Lett. 86, 3196–3199 (2001).

  10. 10.

    , , , & Catastrophic cascade of failures in interdependent networks. Nature 464, 1025–1028 (2010).

  11. 11.

    , , & Robustness of a network of networks. Phys. Rev. Lett. 107, 195701 (2011).

  12. 12.

    , , , & Robustness of interdependent networks under targeted attack. Phys. Rev. E 83, 065101 (2011).

  13. 13.

    , , & Robustness of a network formed by n interdependent networks with a one-to-one correspondence of dependent nodes. Phys. Rev. E 85, 066134 (2012).

  14. 14.

    , & Synchronization in interdependent networks. Chaos 21, 025106 (2011).

  15. 15.

    & Transport on coupled spatial networks. Phys. Rev. Lett. 109, 128703 (2012).

  16. 16.

    , & Evolution of public cooperation on interdependent networks: The impact of biased utility functions. Europhys. Lett. 97, 48001 (2012).

  17. 17.

    , , & Evolution of cooperation in multiplex networks. Sci. Rep. 2, 620 (2012).

  18. 18.

    & Spreading on networks: A topographic view. Complexus 3, 131–146 (2006).

  19. 19.

    , & Epidemics on interconnected networks. Phys. Rev. E 85, 066109 (2012).

  20. 20.

    , & Epidemic spreading on interconnected networks. Phys. Rev. E 86, 026106 (2012).

  21. 21.

    & Analysis of complex contagions in random multiplex networks. Phys. Rev. E 86, 036103 (2012).

  22. 22.

    , , & Networks formed from interdependent networks. Nature Phys. 8, 40–48 (2012).

  23. 23.

    , & Suppressing cascades of load in interdependent networks. Proc. Natl Acad. Sci. USA 109, E680–E689 (2012).

  24. 24.

    , , , & Investigating the topology of interacting networks. Eur. Phys. J. B 84, 635–651 (2011).

  25. 25.

    When networks network. ScienceNews 182, 18 (2012).

  26. 26.

    Networks: An Introduction (Oxford Univ. Press, 2010).

  27. 27.

    , & Evolutionary dynamics on networks of selectively neutral genotypes: Effects of topology and sequence stability. Phys. Rev. E 80, 066112 (2009).

  28. 28.

    Brief comments on perturbation theory of a nonsymmetric matrix: The GF matrix. J. Phys. Chem. A 105, 2612–2616 (2001).

  29. 29.

    , & Characterizing the dynamical importance of network nodes and links. Phys. Rev. Lett. 97, 094102 (2006).

  30. 30.

    & Identifying the role that animals play in their social networks. Proc. R. Soc. Lond. B 271, S477–S481 (2004).

Download references

Acknowledgements

The authors acknowledge the assistance of D. Peralta-Salas in the analytical computations, fruitful conversations with A. Arenas, S. Boccaletti, C. Briones, J. A. Capitán, F. del-Pozo, J. García-Ojalvo, J. Iranzo, C. Lugo, S. C. Manrubia, M. Moreno, Y. Moreno, G. Munoz-Caro and A. Pons, and the support of the Spanish Ministerio de Ciencia e Innovación and Ministerio de Economía y Competitividad under projects FIS2009-07072, FIS2011-27569 and MOSAICO, and of Comunidad de Madrid (Spain) under Project MODELICO-CM S2009ESP-1691.

Author information

Affiliations

  1. Centro de Astrobiología, CSIC-INTA, ctra. de Ajalvir km 4, 28850 Torrejón de Ardoz, Madrid, Spain

    • J. Aguirre
  2. Center for Biomedical Technology (UPM), Campus de Montegancedo, 28223 Pozuelo de Alarcon, Madrid, Spain

    • D. Papo
    •  & J. M. Buldú
  3. Complex Systems Group, URJC, C/Tulipán s/n, 28923 Móstoles, Spain

    • J. M. Buldú

Authors

  1. Search for J. Aguirre in:

  2. Search for D. Papo in:

  3. Search for J. M. Buldú in:

Contributions

J.A. and J.M.B. had the idea behind the new methodology proposed in the paper. J.A. and J.M.B. developed the theory and performed the numerical simulations. J.A., J.M.B. and D.P. participated in the motivation and discussion of the results. J.A., J.M.B. and D.P. wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to J. Aguirre or J. M. Buldú.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    Supplementary Information

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nphys2556

Further reading