Network formation and pairwise stability: A new oddness theorem

Philippe Bich () and Julien Fixary ()
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Philippe Bich: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Julien Fixary: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: We prove that for large classes of polynomial payoff functions, there exist generically an odd number of pairwise stable networks, as a consequence of the topological structure of the graph of pairwise stable weighted networks, which we characterize. This improves recent results in Bich and Morhaim (2020) or in Herings and Zhan (2022), and can be applied to many existing models, as for example to the public good provision model of Bramoullé and Kranton (2007), the information transmission model of Calvó-Armengol and İlkılıç (2009) or the two-way flow model of Bala and Goyal (2000).

Keywords: Weighted networks; Pairwise stable networks; Structure theorem; Generic oddness (search for similar items in EconPapers)
Date: 2022-12
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Citations: View citations in EconPapers (1)

Published in Journal of Mathematical Economics, 2022, 103, ⟨10.1016/j.jmateco.2022.102767⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03969600

DOI: 10.1016/j.jmateco.2022.102767

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