Imitating the Most Successful Neighbor in Social Networks

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, where they are not aware of the relative profitability of their alternative choices. They choose repeatedly from a common set of actions with uncertain payoffs and observe the actions chosen by their neighbors, as well as the payoffs that they received. In each period, they update their choice myopically, imitating the choice of their most successful neighbor in the preceding period. 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 can never be predicted which this state is going to be. 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 exists more than one such action, we provide an additional sufficient condition in the payoff structure, which ensures convergence to a monomorphic steady state for any network. Furthermore, we show that without the assumption of bounded neighborhoods, (i) an action can survive even if only a single agent chooses it initially, and (ii) a network can be in steady state without this being monomorphic