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A characterization of stochastically stable networks

  • TERCIEUX, Olivier
  • VANNETELBOSCH, Vincent

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.

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File URL: http://dx.doi.org/10.1007/s00182-006-0024-7
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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -1877.

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Handle: RePEc:cor:louvrp:-1877
Note: In : International Journal of Game Theory, 34, 351-369, 2006
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  1. van Damme, E.E.C. & Weibull, J., 2002. "Evolution in games with endogenous mistake probabilities," Other publications TiSEM 1c779ce9-9daa-4893-9ddb-e, Tilburg University, School of Economics and Management.
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