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The computation of pairwise stable networks

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  • Herings, P. Jean-Jacques

    (RS: GSBE Theme Data-Driven Decision-Making, RS: GSBE Theme Conflict & Cooperation, Microeconomics & Public Economics)

  • Zhan, Yang

Abstract

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.

Suggested Citation

  • Herings, P. Jean-Jacques & Zhan, Yang, 2021. "The computation of pairwise stable networks," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2021004
    DOI: 10.26481/umagsb.2021004
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    References listed on IDEAS

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    Cited by:

    1. Philippe Bich & Julien Fixary, 2021. "Structure and oddness theorems for pairwise stable networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03287524, HAL.
    2. Philippe Bich & Julien Fixary, 2021. "Structure and oddness theorems for pairwise stable networks," Post-Print halshs-03287524, HAL.

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