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Structure and oddness theorems for pairwise stable networks

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Abstract

We determine the topological structure of the graph of pairwise stable weighted networks. As an application, we obtain that for large classes of polynomial payoff functions, there exists generically and odd number of pairwise stable networks. This improves the results in Bich and Morhaim ([5] or in Herings and Zhan ([14]), and can be applied to many existing models, as for example to the public good provision model of Bramoullé and Kranton ([8]), the information transmission model of Calvó-Armengol ([9]), the two-way flow model of Bala and Goyal ([2]), or Zenou-Ballester's key-player model ([3])

Suggested Citation

  • Philippe Bich & Julien Fixary, 2021. "Structure and oddness theorems for pairwise stable networks," Documents de travail du Centre d'Economie de la Sorbonne 21016, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:21016
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    File URL: http://mse.univ-paris1.fr/pub/mse/CES2021/21016.pdf
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    File URL: https://halshs.archives-ouvertes.fr/halshs-03287524
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    Cited by:

    1. Philippe Bich & Julien Fixary, 2021. "Oddness of the number of Nash equilibria: the case of polynomial payoff functions," Post-Print halshs-03354269, HAL.
    2. Philippe Bich & Julien Fixary, 2021. "Oddness of the number of Nash equilibria: the Case of Polynomial Payoff Functions," Documents de travail du Centre d'Economie de la Sorbonne 21027, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Philippe Bich & Julien Fixary, 2021. "Oddness of the number of Nash equilibria: the case of polynomial payoff functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03354269, HAL.

    More about this item

    Keywords

    Weighted Networks; Pairwise Stable Networks Correspondence; Generic Oddness;
    All these keywords.

    JEL classification:

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

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