Imitating the Most Successful Neighbor in Social Networks

We consider a model of observational learning in social networks. At every period, all agents choose from the same set of actions with uncertain payoffs and observe the actions chosen by their neighbors, as well as the payoffs they received. They update their choice myopically, by imitating the choice of their most successful neighbor. We show that in finite networks, regardless of the structure, the population converges to a monomorphic steady state, i.e. one at which every agent chooses the same action. Moreover, in arbitrarily large networks with bounded neighborhoods, an action is diffused to the whole population if it is the only one chosen initially by a non--negligible share of the population. If there exist more than one such actions, we provide an additional sufficient condition in the payoff structure, which ensures convergence to a monomorphic steady state for all networks. Furthermore, we show that without the assumption of bounded neighborhoods, (i) an action can survive even if it is initially chosen by a single agent, and (ii) a network can be in steady state without this being monomorphic