A Characterization of Stochastically Stable Networks

Vincent Vannetelbosch and Olivier Tercieux

No 2005.48, Working Papers from Fondazione Eni Enrico Mattei

Abstract: Jackson and Watts [J. of Econ. Theory 71 (2002), 44-74] have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, p-pairwise stability, which allows us to characterize the stochastically stable networks without requiring the "tree construction" and the computation of resistance that may be quite complex. When a 1/2-pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of p-pairwise stable networks, we define its set-valued extension with the notion of p-pairwise stable set. The 1/2-pairwise stable set exists and is unique. Any stochastically stable network is included in the 1/2-pairwise stable set. Thus, any network outside the 1/2-pairwise stable set must be considered as a nonrobust network. We also show that the 1/2-pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more "stable" than a pairwise stable network.

Keywords: Network formation; Pairwise stability; Stochastic stability (search for similar items in EconPapers)
JEL-codes: C70 D20 (search for similar items in EconPapers)
Date: 2005-04
New Economics Papers: this item is included in nep-gth and nep-net
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Related works:
Journal Article: A characterization of stochastically stable networks (2006)
Working Paper: A characterization of stochastically stable networks (2006)
Working Paper: A characterization of stochastically stable networks (2006)
Working Paper: A characterization of stochastically stable networks (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:fem:femwpa:2005.48

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