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Hypergraph Formation Game

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  • Jun, Tackseung
  • Kim, Jeong-Yoo

Abstract

We define a hypergraph by a set of associations which consist of nonexclusive two or more players. It is a generalization of a graph (or a network) in the sense that an association, the counterpart of a link in a hypergraph, connects any number of nodes, not simply a pair of nodes. We characterize the efficient hypergraphs and stable hypergraphs for the linear variable cost of associations. The efficient hypergraph is either the empty hypergraph or the grand hypergraph consisting of a single grand association. The stable hypergraph can be a grand hypergraph, a star hypergraph or a line hypergraph. If a star hypergraph is stable, it must have a singleton center. Generally, a hypergraph can be underconnected, but cannot be overconnected.

Suggested Citation

  • Jun, Tackseung & Kim, Jeong-Yoo, 2009. "Hypergraph Formation Game," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 50(2), pages 1-16, December.
    • Handle: RePEc:hit:hitjec:v:50:y:2009:i:2:p:1-16
    DOI: 10.15057/18044
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    References listed on IDEAS

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    Cited by:

    1. Fershtman, Chaim & Persitz, Dotan, 2018. "Social Clubs and Social Networks," CEPR Discussion Papers 12874, C.E.P.R. Discussion Papers.

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    More about this item

    Keywords

    Association; Efficiency; Hypergraph; Network; Stability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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