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A hierarchical network formation model

Author

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  • 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
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    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.
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    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

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