Network formation and pairwise stability: A new oddness theorem

Philippe Bich and Julien Fixary

Journal of Mathematical Economics, 2022, vol. 103, issue C

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
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:103:y:2022:i:c:s0304406822000933

DOI: 10.1016/j.jmateco.2022.102767

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