A Characterization of Stochastically Stable Networks
01.01.2005
Vincent Vannetelbosch, Olivier Tercieux
C70,D20
Network formation,Pairwise stability,Stochastic stability
Climate Change and Sustainable Development
Carlo Carraro
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, pโpairwise 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 1/2โpairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of pโpairwise stable networks, we define its set-valued extension with the notion of pโpairwise stable set. The 1/2โpairwise stable set exists and is unique. Any stochastically stable network is included in the 1/2โpairwise stable set. Thus, any network outside the 1/2โpairwise stable set must be considered as a nonrobust network. We also show that the 1/2โpairwise 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.