Imitating the Most Successful Neighbor in Social Networks

Abstract We study a model of observational learning in a set of agents who are connected through a social network. The agents face identical decision problems under uncertainty and update their choices myopically, imitating the choice of their most successful neighbor. We show that in finite networks, regardless of the network structure, the population converges to a monomorphic steady state, i.e., one at which every agent chooses the same action, and it cannot be predicted which this action will be. In arbitrarily large networks with bounded neighborhoods, an action is diffused to the whole population either if it is the only one initially chosen by a non-negligible share of the population, or if the payoffs satisfy a sufficient condition. Without the assumption of bounded neighborhoods, (i) an action can survive even if only one agent chooses it initially, and (ii) there may exist steady states that are not monomorphic.