Local Interactions on Graphs: A Pairwise Approximation Approach∗

This paper analyzes a dynamic model of local interactions on a graph. Interactions are of the threshold type, i.e. agents choose to match the majority choice of direct neighbors. Rather than a mean-field model we use a pairwise approximation to model the dynamics of the system. Thus we consider correlations of linked nodes ’ states. In contrast to the meanfield model we find a continuum of steady states depending on initial conditions, to the extent that states cannot become extinct for graphs with low degrees. Entry is facilitated by targeting nodes with low degree or the smallest incumbent state.