The computation of pairwise stable networks

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1 Citation (Scopus)


One of the most important stability concepts for network formation is pairwise stability. We develop a homotopy algorithm that is effective in computing pairwise stable networks for a generic network formation problem. To do so, we reformulate the concept of pairwise stability as a Nash equilibrium of a non-cooperative game played by the links in the network and adapt the linear tracing procedure for non-cooperative games to the network formation problem. As a by-product of our main result, we obtain that the number of pairwise stable networks is generically odd. We apply the algorithm to the connections model and obtain a number of novel insights.
Original languageEnglish
JournalMathematical Programming
Publication statusE-pub ahead of print - 14 Mar 2022


  • Computation of equilibria
  • Connections model
  • Pairwise stable network
  • Tracing procedure


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