A characterization of stochastically stable networks

Tercieux, Olivier;Vannetelbosch, Vincent
(2006) International Journal of Game Theory — Vol. 34, n° 3, p. 351-369 (2006)

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Abstract
Jackson and Watts (J Econ Theory 71: 44–74, 2002) 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 networks is included in the 1/2-pairwise stable set. Thus, any network outside the 1/2-pairwise stable set must be considered as a non-robust 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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Tercieux, O., & Vannetelbosch, V. (2006). A characterization of stochastically stable networks. International Journal of Game Theory, 34(3), 351-369. https://doi.org/10.1007/s00182-006-0024-7 (Original work published 2006)