Network formation and pairwise stability: A new oddness theorem

Journal article: 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).

Author(s)

Philippe Bich, Julien Fixary

Journal
  • Journal of Mathematical Economics
Date of publication
  • 2022
Keywords
  • Weighted networks
  • Pairwise stable networks
  • Structure theorem
  • Generic oddness
Version
  • 1
Volume
  • 103