Structure and oddness theorems for pairwise stable networks

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, UP1 - Université Paris 1 Panthéon-Sorbonne, 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: UP1 - Université Paris 1 Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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 an 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]).

Keywords: Weighted Networks; Pairwise Stable Networks Correspondence; Generic oddness (search for similar items in EconPapers)
Date: 2021-06
New Economics Papers: this item is included in nep-gth, nep-isf and nep-net
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03287524v1
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Published in 2021

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