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A characterization of stochastically stable networks

Author

Listed:
  • Olivier Tercieux

    (PJSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique)

  • Vincent Vannetelbosch

    (FNRS - Fonds de la Recherche Scientifique - Fonds de la Recherche Scientifique [FNRS], CORE - Center of Operation Research and Econometrics [Louvain] - UCL - Université Catholique de Louvain = Catholic University of Louvain)

Abstract

ackson and Watts (J Econ Theory 71: 44-74, 2002) have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, p-pairwise stability, which allows us to characterize the stochastically stable networks without requiring the "tree construction" and the computation of resistance that may be quite complex. When a 1/2 -pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of p-pairwise stable networks, we define its set-valued extension with the notion of p-pairwise stable set. The 1/2 -pairwise stable set exists and is unique. Any stochastically stable networks is included in the 1/2 -pairwise stable set. Thus, any network outside the 1/2 -pairwise stable set must be considered as a non-robust network. We also show that the 1/2 -pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more "stable" than a pairwise stable network.

Suggested Citation

  • Olivier Tercieux & Vincent Vannetelbosch, 2006. "A characterization of stochastically stable networks," Post-Print halshs-00754134, HAL.
    • Handle: RePEc:hal:journl:halshs-00754134
    DOI: 10.1007/s00182-006-0024-7
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    Cited by:

    1. Herings, P. Jean-Jacques & Mauleon, Ana & Vannetelbosch, Vincent, 2009. "Farsightedly stable networks," Games and Economic Behavior, Elsevier, vol. 67(2), pages 526-541, November.
    2. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    3. Yasunori Okumura, 2011. "A dynamic analysis of collusive networks," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 317-336, December.
    4. Britta Hoyer & Stephanie Rosenkranz, 2018. "Determinants of Equilibrium Selection in Network Formation: An Experiment," Games, MDPI, vol. 9(4), pages 1-25, November.
    5. Marco Mantovani & Georg Kirchsteiger & Ana Mauleon & Vincent Vannetelbosch, 2011. "Myopic or Farsighted? An Experiment on Network Formation," Working Papers 2011.45, Fondazione Eni Enrico Mattei.
    6. Joost Vandenbossche & Thomas Demuynck, 2013. "Network Formation with Heterogeneous Agents and Absolute Friction," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 23-45, June.
    7. Pierre de Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2024. "Local farsightedness in network formation," International Journal of Economic Theory, The International Society for Economic Theory, vol. 20(2), pages 199-226, June.
    8. Kirchsteiger, Georg & Mantovani, Marco & Mauleon, Ana & Vannetelbosch, Vincent, 2016. "Limited farsightedness in network formation," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 97-120.
    9. Pierre de Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2023. "Myopic-farsighted absorbing networks," Theory and Decision, Springer, vol. 94(3), pages 405-422, April.
    10. Filippo Vergara Caffarelli, 2009. "Networks with decreasing returns to linking," Temi di discussione (Economic working papers) 734, Bank of Italy, Economic Research and International Relations Area.

    More about this item

    Keywords

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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D20 - Microeconomics - - Production and Organizations - - - General

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