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On the existence of Pairwise stable weighted networks

Author

Listed:
  • Philippe Bich

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Lisa Morhaim

    (CRED - Centre de Recherche en Economie et Droit - UP2 - Université Panthéon-Assas)

Abstract

In network theory, Jackson and Wolinsky introduced a now widely used notion of stability for unweighted network formation called pairwise stability. We prove the existence of pairwise stable weighted networks under assumptions on payoffs that are similar to those in Nash's and Glicksberg's existence theorem (continuity and quasi concavity). Then, we extend our result, allowing payoffs to depend not only on the network, but also on some game-theoretic strategies. The proof is not a standard application of tools from game theory, the difficulty coming from the fact that the pairwise stability notion has both cooperative and noncooperative features. Last, some examples are given and illustrate how our results may open new paths in the literature on network formation.

Suggested Citation

  • Philippe Bich & Lisa Morhaim, 2020. "On the existence of Pairwise stable weighted networks," PSE-Ecole d'économie de Paris (Postprint) halshs-03969712, HAL.
    • Handle: RePEc:hal:pseptp:halshs-03969712
    DOI: 10.1287/moor.2019.1032
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    Citations

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    Cited by:

    1. John Higgins & Tarun Sabarwal, 2021. "Control and Spread of Contagion in Networks," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202111, University of Kansas, Department of Economics.
    2. Bich, Philippe & Teteryatnikova, Mariya, 2023. "On perfect pairwise stable networks," Journal of Economic Theory, Elsevier, vol. 207(C).
    3. Herings, P.J.J., 2024. "Globally and Universally Convergent Price Adjustment Processes," Other publications TiSEM 12dc4fc2-19e8-4a8c-b2ff-2, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    Pairwise Stable Network; Weighted Network;

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