Stability of Agreement in State-dependent Interaction Environments

Abstract

We study stochastic stability for a class of agreement dynamics and define two forms of agreement which we call stochastic agreement and stochastic absolute agreement. We identify conditions for a broad class of random, possibly state-dependent agreement processes to achieve stochastic agreement. We take the approach of applying Lyapunov drift criteria to study the behaviour of such processes. We generalize some results in the literature to the noisy and state-dependent case.