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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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    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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