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A model of the formation of multilayer networks

Author

Listed:
  • Billand, Pascal
  • Bravard, Christophe
  • Joshi, Sumit
  • Mahmud, Ahmed Saber
  • Sarangi, Sudipta

Abstract

We study the formation of multilayer networks where payoffs are determined by the degrees of players in each network. We begin by imposing either concavity or convexity in degree on the payoff function of the players. We then explore distinct network relationships that result from inter- and intra-network spillovers captured by the properties of supermodularity/submodularity and strategic complementarity respectively. We show the existence of equilibria and characterize them. Additionally, we establish both necessary and sufficient conditions for an equilibrium to occur. We also highlight the connection, in equilibrium, between inter-network externalities and the identity of linked players in one network given the identity of linked players in the other network. Furthermore, we analyze efficient multilayer networks. Finally, we extend our models to contexts with more than two layers, and scenarios where agents receive a bonus for being connected to the same individuals in both networks.

Suggested Citation

  • Billand, Pascal & Bravard, Christophe & Joshi, Sumit & Mahmud, Ahmed Saber & Sarangi, Sudipta, 2023. "A model of the formation of multilayer networks," Journal of Economic Theory, Elsevier, vol. 213(C).
    • Handle: RePEc:eee:jetheo:v:213:y:2023:i:c:s002205312300114x
    DOI: 10.1016/j.jet.2023.105718
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    References listed on IDEAS

    as
    1. Matthew O. Jackson & Stephen Nei, 2014. "Networks of Military Alliances, Wars, and International Trade," Working Papers 2014.46, Fondazione Eni Enrico Mattei.
    2. Bramoullé, Yann & Kranton, Rachel, 2007. "Risk-sharing networks," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 275-294.
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    4. Christophe Bravard & Sudipta Sarangi & PASCAL BILLAND & CHRISTOPHE BRAVARD & SUBHADIP CHAKRABARTI & SUDIPTA SARANGI, 2016. "Business Intelligence and Multimarket Competition," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(2), pages 248-267, April.
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    6. Goyal, Sanjeev & Joshi, Sumit, 2003. "Networks of collaboration in oligopoly," Games and Economic Behavior, Elsevier, vol. 43(1), pages 57-85, April.
    7. Aditi Roy & Sudipta Sarangi, 2009. "Revisiting Friendship Networks," Economics Bulletin, AccessEcon, vol. 29(4), pages 2640-2647.
    8. Hector Tzavellas, 2023. "A Multilayer View Of Systemic Importance And Aggregate Fluctuations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 1023-1046, August.
    9. Joshi, Sumit & Mahmud, Ahmed Saber & Sarangi, Sudipta, 2020. "Network formation with multigraphs and strategic complementarities," Journal of Economic Theory, Elsevier, vol. 188(C).
    10. Walsh, A. M., 2019. "Games on Multi-Layer Networks," Cambridge Working Papers in Economics 1954, Faculty of Economics, University of Cambridge.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Mauleon, Ana & Nanumyan, Mariam & Vannetelbosch, Vincent, 2024. "Ideal efforts and consensus in a multi-layer network game," LIDAM Discussion Papers CORE 2024023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Devine, Peter & Joshi, Sumit & Mahmud, Ahmed Saber, 2024. "Alliance formation in a multipolar world," Journal of Economic Behavior & Organization, Elsevier, vol. 223(C), pages 248-277.

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    More about this item

    Keywords

    Multilayer networks; Concavity; Convexity; Supermodularity; Submodularity;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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