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Interaction on Hypergraphs

Author

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  • Philippe Solal

    (CREUSET - Centre de Recherche Economique de l'Université de Saint-Etienne - UJM - Université Jean Monnet - Saint-Étienne)

  • Jacques Durieu

    (CREUSET - Centre de Recherche Economique de l'Université de Saint-Etienne - UJM - Université Jean Monnet - Saint-Étienne)

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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Suggested Citation

  • Philippe Solal & Jacques Durieu, 2005. "Interaction on Hypergraphs," Post-Print hal-00375568, HAL.
    • Handle: RePEc:hal:journl:hal-00375568
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    References listed on IDEAS

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    1. Richard Baron & Jacques Durieu & Hans Haller & Philippe Solal, 2003. "Control costs and potential functions for spatial games," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(4), pages 541-561, September.
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    Cited by:

    1. Nathalie Jorzik & Frank Mueller‐Langer, 2020. "Multilateral stability and efficiency of trade agreements: A network formation approach," The World Economy, Wiley Blackwell, vol. 43(2), pages 355-370, February.

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    More about this item

    JEL classification:

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

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