On the existence of Pairwise stable weighted networks

Philippe Bich () and Lisa Morhaim
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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
Lisa Morhaim: CRED - Centre de Recherche en Economie et Droit - UP2 - Université Panthéon-Assas

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

Abstract: In network theory, Jackson and Wolinsky introduced a now widely used notion of stability for unweighted network formation called pairwise stability. We prove the existence of pairwise stable weighted networks under assumptions on payoffs that are similar to those in Nash's and Glicksberg's existence theorem (continuity and quasi concavity). Then, we extend our result, allowing payoffs to depend not only on the network, but also on some game-theoretic strategies. The proof is not a standard application of tools from game theory, the difficulty coming from the fact that the pairwise stability notion has both cooperative and noncooperative features. Last, some examples are given and illustrate how our results may open new paths in the literature on network formation.

Keywords: Pairwise Stable Network; Weighted Network (search for similar items in EconPapers)
Date: 2020-11
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Citations: View citations in EconPapers (5)

Published in Mathematics of Operations Research, 2020, 45 (4), pp.1393-1404. ⟨10.1287/moor.2019.1032⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-03969712

DOI: 10.1287/moor.2019.1032

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