A characterization of stochastically stable networks

Abstract

ackson 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 networks without requiring the tree construction and the computation of resistance that may be quite complex. When a 1/2 -pairwise network exists, it is unique and it coincides with the unique stochastically network. To solve the inexistence problem of p-pairwise networks, we define its set-valued extension with the notion of p-pairwise set. The 1/2 -pairwise set exists and is unique. Any stochastically networks is included in the 1/2 -pairwise set. Thus, any network outside the 1/2 -pairwise set must be considered as a non-robust network. We also show that the 1/2 -pairwise set can contain no pairwise network and we provide examples where a set of networks is more stable than a pairwise network.