IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/62551.html
   My bibliography  Save this paper

A hierarchical network formation model

Author

Listed:
  • Atabati, Omid
  • Farzad, Babak

Abstract

We present a network formation model based on a particularly interesting class of networks in social settings, where individuals' positions are determined according to a topic-based or hierarchical taxonomy. In this game-theoretic model, players are located in the leaves of a complete b-ary tree as the seed network with the objective of minimizing their collective distances to others in the network. In the grid-based model of Even-Dar and Kearns [3], they demonstrate the existence of small diameter networks with the threshold of a = 2 where the cost of a new link depends on the distance between the two endpoints to the power of a. We show the appearance of small diameter equilibrium networks with the threshold of a = 1/4 in the hierarchical or tree-based networks. Moreover, the general set of equilibrium networks in our model are guaranteed to exist and they are pairwise Nash stable with transfers [2].

Suggested Citation

  • Atabati, Omid & Farzad, Babak, 2015. "A hierarchical network formation model," MPRA Paper 62551, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:62551
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/62551/1/MPRA_paper_62551.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Francis Bloch & Matthew Jackson, 2006. "Definitions of equilibrium in network formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 305-318, October.
    2. Atabati, Omid & Farzad, Babak, 2014. "A strategic model for network formation," MPRA Paper 62529, University Library of Munich, Germany.
    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. 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.
    2. Péter Bayer & Ani Guerdjikova, 2020. "Optimism leads to optimality: Ambiguity in network formation," Working Papers hal-03005107, HAL.
    3. Kets, W., 2008. "Beliefs in Network Games (Revised version of CentER DP 2007-46)," Other publications TiSEM a08e38fd-6b00-4233-94ce-3, Tilburg University, School of Economics and Management.
    4. Karbowski, Adam, 2009. "Sieci społeczne i technologiczne: wpływ na proces powstawania innowacji w gospodarce [Social and Technological Networks and its Effects on Innovation Dynamics]," MPRA Paper 73624, University Library of Munich, Germany.
    5. Swapnil Dhamal & Y. Narahari, 2015. "Formation of Stable Strategic Networks with Desired Topologies," Studies in Microeconomics, , vol. 3(2), pages 158-213, December.
    6. Matthew O. Jackson & Stephen Nei, 2014. "Networks of Military Alliances, Wars, and International Trade," Working Papers 2014.46, Fondazione Eni Enrico Mattei.
    7. Kets, W., 2007. "Convergence of Beliefs in Bayesian Network Games," Other publications TiSEM 372c88bd-4b09-4976-a6e2-4, Tilburg University, School of Economics and Management.
    8. Gallo Edoardo, 2012. "Small World Networks with Segregation Patterns and Brokers," Review of Network Economics, De Gruyter, vol. 11(3), pages 1-46, September.
    9. Hellmann, Tim & Staudigl, Mathias, 2014. "Evolution of social networks," European Journal of Operational Research, Elsevier, vol. 234(3), pages 583-596.
    10. Áureo de Paula, 2020. "Econometric Models of Network Formation," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 775-799, August.
    11. Alex Centeno, 2022. "A Structural Model for Detecting Communities in Networks," Papers 2209.08380, arXiv.org, revised Oct 2022.
    12. à ureo de Paula & Seth Richards†Shubik & Elie Tamer, 2018. "Identifying Preferences in Networks With Bounded Degree," Econometrica, Econometric Society, vol. 86(1), pages 263-288, January.
    13. Bryan S. Graham, 2019. "Network Data," Papers 1912.06346, arXiv.org.
    14. Norma Olaizola & Federico Valenciano, 2016. "From bilateral two-way to unilateral one-way flow link-formation," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(2), pages 257-278, June.
    15. Alan Griffith, 2022. "A continuous model of strong and weak ties," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(6), pages 1519-1563, December.
    16. Bloch, Francis & Dutta, Bhaskar, 2009. "Communication networks with endogenous link strength," Games and Economic Behavior, Elsevier, vol. 66(1), pages 39-56, May.
    17. Daniel E. May, 2015. "Inefficient Stable International Trade Networks," Studies in Microeconomics, , vol. 3(1), pages 13-34, June.
    18. Rahmi İlkılıç & Hüseyin İkizler, 2019. "Equilibrium refinements for the network formation game," Review of Economic Design, Springer;Society for Economic Design, vol. 23(1), pages 13-25, June.
    19. Miettinen, Topi & Poutvaara, Panu, 2014. "A market for connections," European Journal of Political Economy, Elsevier, vol. 33(C), pages 37-52.
    20. Olaizola, By Norma & Valenciano, Federico, 2021. "Efficiency and stability in the connections model with heterogeneous nodes," Journal of Economic Behavior & Organization, Elsevier, vol. 189(C), pages 490-503.

    More about this item

    Keywords

    Network formation; Hierarchical networks; Linking game;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:62551. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.