Structure and oddness theorems for pairwise stable networks
Résumé
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]).
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