Testable Implication of Pairwise Stability in Networks

Abstract

This paper characterizes when an observed network is rationalizable as pairwise stable -- that there exist preferences such that no pairs of individuals would deviate from the existing network structure by unilaterally dissolving links, or bilaterally forming links. I show that the Weak Axiom of Revealed Pairwise Stability (WARPS) is a necessary and sufficient testable condition for pairwise stability. WARPS is an algorithm that checks the network for cycles in the revealed preference relations by perturbing the network and checking for isomorphism between pairs of nodes. Based on this, I introduce a novel network property called the network stability score. I calculate the stability scores for real-world networks (Banerjee et al. (2013)), and investigate the extent to which they can be rationalized as pairwise stable. I find that the stability score is lower in networks where individuals travel frequently outside of the network. I show that network stability is related to diffusion -- when the stability score is low, it is less effective to target central nodes in the network as a seeding strategy

Keywords: Revealed preference, Networks formation, Non-parametric identification, Social networks, Pairwise stability, Testable implications, Graph isomorphism