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Interaction on Hypergraphs

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Author Info

  • Durieu, Jacques

    (CREUSET, University of Saint-Etienne)

  • Haller, Hans

    ()
    (Department of Economics, Virginia Polytechnic Institute and State University)

  • Solal, Philippe

    (CREUSET, University of Saint-Etienne)

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    Abstract

    Interaction on hypergraphs generalizes interaction on graphs, also known as pairwise local interaction. For games played on a hypergraph which are supermodular potential games, logit-perturbed best-response dynamics are studied. We find that the associated stochastically stable states form a sublattice of the lattice of Nash equilibria and derive comparative statics results for the smallest and the largest stochastically stable state. In the special case of networking games, we obtain comparative statics results with respect to investment costs, for Nash equilibria of supermodular games as well as for Nash equilibria of submodular games.

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    File URL: http://www.sfb504.uni-mannheim.de/publications/dp05-34.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number 05-34.

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    Length: 27 pages
    Date of creation: 22 Oct 2005
    Date of revision:
    Handle: RePEc:xrs:sfbmaa:05-34

    Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged. This paper was written while Hans Haller was visiting the SFB 504, University of Mannheim.
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    References

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    1. Kaarboe, O.M. & Tieman, A.F., 2000. "Equilibrium Selection in Games with Macroeconomic Complementarities," Norway; Department of Economics, University of Bergen, Department of Economics, University of Bergen 2199, Department of Economics, University of Bergen.
    2. Larry E. Blume, 1996. "Population Games," Working Papers, Santa Fe Institute 96-04-022, Santa Fe Institute.
    3. Echenique, Federico & Sabarwal, Tarun, 2003. "Strong comparative statics of equilibria," Games and Economic Behavior, Elsevier, vol. 42(2), pages 307-314, February.
    4. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, Springer, vol. 26(3), pages 497-516, October.
    5. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
    6. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
    7. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers, Stanford - Institute for Thoretical Economics 11, Stanford - Institute for Thoretical Economics.
    8. Burkhard Schipper, 2002. "Submodularity and the Evolution of Walrasian Behavior," Bonn Econ Discussion Papers, University of Bonn, Germany bgse4_2003, University of Bonn, Germany.
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    Cited by:
    1. Jorzik, Nathalie & Mueller-Langer, Frank, 2013. "Multilateral Stability and Efficiency of Trade Agreements: A Network Formation Approach," Discussion Papers in Economics 14587, University of Munich, Department of Economics.

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