A Characterization of Stochastically Stable Networks

30 Pages Posted: 12 Apr 2005

See all articles by Vincent J. Vannetelbosch

Vincent J. Vannetelbosch

Center for Operations Research and Econometrics (CORE)

Olivier Tercieux

Paris-Jourdan Sciences Economiques (PSE)

Date Written: April 2005

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

JEL Classification: C70, D20

Suggested Citation

Vannetelbosch, Vincent J. and Tercieux, Olivier, A Characterization of Stochastically Stable Networks (April 2005). Available at SSRN: https://ssrn.com/abstract=700605 or http://dx.doi.org/10.2139/ssrn.700605

Vincent J. Vannetelbosch (Contact Author)

Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
1348 Louvain-la-Neuve, 1348
Belgium

Olivier Tercieux

Paris-Jourdan Sciences Economiques (PSE) ( email )

48, BD Jourdan
75014 Paris
France

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