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Network Formation with Multigraphs and Strategic Complementarities

Author

Listed:
  • Sumit Joshi

    (George Washington University)

  • Sudipta Sarangi

    (Virginia Tech)

  • Ahmed Saber Mahmud

    (Johns Hopkins University)

Abstract

Economic agents are typically connected to others in multiple network relationships, and the archi- tecture of one network could be shaped by connections in other networks. This paper examines the formation of one network when connections in a second network are inherited under two scenarios: (i) the inherited network is asymmetric allowing for a wide range of graphs called nested split graphs, and (ii) the inherited network is a symmetric type of network belonging to a subclass of regular graphs. Both the inherited and endogenously formed networks are interdependent because the respective actions in each are (weak) strategic complements. This property is su¢ cient to show that those who inherit high centrality will continue to have high centrality. Additionally, the network formed by the agents induces a coarser partition than the inherited network, suggesting the possibility of being able to improve network centrality, but only in a limited manner. Thus, our analysis explains preferential attachment and why inequality is often entrenched in society, how asymmetries in one network may be magniÖed or diminished in another, and what determines the identity of players occupying the various vertices of asymmetric equilibrium networks.

Suggested Citation

  • Sumit Joshi & Sudipta Sarangi & Ahmed Saber Mahmud, 2017. "Network Formation with Multigraphs and Strategic Complementarities," Working Papers 2017-27, The George Washington University, Institute for International Economic Policy.
    • Handle: RePEc:gwi:wpaper:2017-27
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    References listed on IDEAS

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    4. Patrick Allmis & Luca Paolo Merlino, 2023. "Homophily and Specialization in Networks," Papers 2312.00457, arXiv.org.

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    More about this item

    Keywords

    Network formation; multigraphs; strategic complementarities; Katz-Bonacich centrality; nested split graphs;
    All these keywords.

    JEL classification:

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

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