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A Characterization of Stochastically Stable Networks

Author

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  • Vincent Vannetelbosch

    (CORE, Université Catholique de Louvain)

  • Olivier Tercieux

    (CentER, Tilburg University)

Abstract

Jackson and Watts [J. of Econ. Theory 71 (2002), 44-74] 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 network is included in the 1/2-pairwise stable set. Thus, any network outside the 1/2-pairwise stable set must be considered as a nonrobust 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

  • Vincent Vannetelbosch & Olivier Tercieux, 2005. "A Characterization of Stochastically Stable Networks," Working Papers 2005.48, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2005.48
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    References listed on IDEAS

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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. Mantovani, Marco & Kirchsteiger, Georg & Mauleon, Ana & Vannetelbosch, Vincent, 2011. "Myopic or Farsighted? An Experiment on Network Formation," Climate Change and Sustainable Development 108256, Fondazione Eni Enrico Mattei (FEEM).
    3. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    4. 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.
    5. 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.
    6. 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.
    7. de Callatay, Pierre & Mauleon, Ana & Vannetelbosch, Vincent, 2023. "Local Farsightedness in Network Formation," LIDAM Discussion Papers CORE 2023003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Pierre de Callataÿ & Ana Mauleon & Vincent Vannetelbosch, 2023. "Myopic-farsighted absorbing networks," Theory and Decision, Springer, vol. 94(3), pages 405-422, April.
    9. Britta Hoyer & Stephanie Rosenkranz, 2018. "Determinants of Equilibrium Selection in Network Formation: An Experiment," Games, MDPI, vol. 9(4), pages 1-25, November.
    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.

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    More about this item

    Keywords

    Network formation; Pairwise stability; Stochastic stability;
    All these keywords.

    JEL classification:

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

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