IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v213y2023ics002205312300114x.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S002205312300114X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2023.105718?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
    2. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    3. Goyal, Sanjeev & Joshi, Sumit, 2003. "Networks of collaboration in oligopoly," Games and Economic Behavior, Elsevier, vol. 43(1), pages 57-85, April.
    4. Jackson, Matthew O. & Nei, Stephen, 2014. "Networks of Military Alliances, Wars, and International Trade," Climate Change and Sustainable Development 172702, Fondazione Eni Enrico Mattei (FEEM).
    5. 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.
    6. Joshi, Sumit & Mahmud, Ahmed Saber & Sarangi, Sudipta, 2020. "Network formation with multigraphs and strategic complementarities," Journal of Economic Theory, Elsevier, vol. 188(C).
    7. Bramoullé, Yann & Kranton, Rachel, 2007. "Risk-sharing networks," Journal of Economic Behavior & Organization, Elsevier, vol. 64(3-4), pages 275-294.
    8. Aditi Roy & Sudipta Sarangi, 2009. "Revisiting Friendship Networks," Economics Bulletin, AccessEcon, vol. 29(4), pages 2640-2647.
    9. 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.
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sanjeev Goyal, 2015. "Networks in Economics: A Perspective on the Literature," Cambridge Working Papers in Economics 1548, Faculty of Economics, University of Cambridge.
    2. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Liu, Xiaodong & Patacchini, Eleonora & Zenou, Yves & Lee, Lung-Fei, 2011. "Criminal Networks: Who is the Key Player?," Research Papers in Economics 2011:7, Stockholm University, Department of Economics.
    4. Joshi, Sumit & Mahmud, Ahmed Saber, 2018. "Unilateral and multilateral sanctions: A network approach," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 52-65.
    5. Michael D. König & Xiaodong Liu & Yves Zenou, 2019. "R&D Networks: Theory, Empirics, and Policy Implications," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 476-491, July.
    6. Michael D König & Stefano Battiston & Mauro Napoletano & Frank Schweitzer, 2008. "The Efficiency and Evolution of R&D Networks," Working Papers hal-00973077, HAL.
    7. Acemoglu, Daron & Malekian, Azarakhsh & Ozdaglar, Asu, 2016. "Network security and contagion," Journal of Economic Theory, Elsevier, vol. 166(C), pages 536-585.
    8. Goyal, S., 2018. "Heterogeneity and Networks," Cambridge Working Papers in Economics 1812, Faculty of Economics, University of Cambridge.
    9. repec:hal:wpspec:info:hdl:2441/9935 is not listed on IDEAS
    10. Carlos Ponce & Flavia Roldán, 2016. "Antitrust policies in network environments," Documentos de Investigación 112, Universidad ORT Uruguay. Facultad de Administración y Ciencias Sociales.
    11. repec:spo:wpecon:info:hdl:2441/9935 is not listed on IDEAS
    12. Antonio Cabrales & Piero Gottardi & Fernando Vega-Redondo, 2017. "Risk Sharing and Contagion in Networks," The Review of Financial Studies, Society for Financial Studies, vol. 30(9), pages 3086-3127.
    13. Belhaj, Mohamed & Bervoets, Sebastian & Deroïan, Frédéric, 2016. "Efficient networks in games with local complementarities," Theoretical Economics, Econometric Society, vol. 11(1), January.
    14. repec:hal:wpspec:info:hdl:2441/7346 is not listed on IDEAS
    15. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    16. Ushchev, Philip & Zenou, Yves, 2018. "Price competition in product variety networks," Games and Economic Behavior, Elsevier, vol. 110(C), pages 226-247.
    17. , D. & Tessone, Claudio J. & ,, 2014. "Nestedness in networks: A theoretical model and some applications," Theoretical Economics, Econometric Society, vol. 9(3), September.
    18. Deng, Liuchun & Sun, Yufeng, 2017. "Criminal network formation and optimal detection policy: The role of cascade of detection," Journal of Economic Behavior & Organization, Elsevier, vol. 141(C), pages 43-63.
    19. repec:hal:wpspec:info:hdl:2441/9933 is not listed on IDEAS
    20. Kor, Ryan & Zhou, Junjie, 2023. "Multi-activity influence and intervention," Games and Economic Behavior, Elsevier, vol. 137(C), pages 91-115.
    21. M. Koenig & Claudio J. Tessone & Yves Zenou, "undated". "A Dynamic Model of Network Formation with Strategic Interactions," Working Papers CCSS-09-006, ETH Zurich, Chair of Systems Design.
    22. Grandjean, G. & Tellone, D. & Vergote, W., 2017. "Endogenous network formation in a Tullock contest," Mathematical Social Sciences, Elsevier, vol. 85(C), pages 1-10.
    23. repec:spo:wpecon:info:hdl:2441/7346 is not listed on IDEAS
    24. Mauleon, Ana & Sempere-Monerris, Jose J. & Vannetelbosch, Vincent J., 2011. "Networks of manufacturers and retailers," Journal of Economic Behavior & Organization, Elsevier, vol. 77(3), pages 351-367, March.
    25. Goyal, S., 2016. "Networks and Markets," Cambridge Working Papers in Economics 1652, Faculty of Economics, University of Cambridge.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:213:y:2023:i:c:s002205312300114x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.