A Characterization of Stochastically Stable Networks
Vincent Vannetelbosch, Olivier Tercieux
Network formation,Pairwise stability,Stochastic stability
Climate Change and Sustainable Development
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.