Multidimensional Social Learning

This paper provides a model of social learning where the order in which actions are taken is determined by an m-dimensional integer lattice rather than along a line as in the herding model. The observation structure is determined by a random network. Every agent links to each of his preceding lattice neighbors independently with probability p, and observes the actions of all agents that are reachable via a directed path in the realized social network. We show that for every α<1 there exists a linkage probability p(α) such that for all p∈(p(α),1), the proportion of agents who take the optimal action in the limit with probability one is at least α, for any signal distribution. By contrast, if signals are bounded and p equals one, all agents select the suboptimal action with positive probability. We further show that asymptotic welfare increases in the lattice dimension m and in the linkage probability p, for p<1. Finally, we identify a property that allows us to rank informative signal distributions in terms of the asymptotic welfare they generate, and we establish the robustness of our main result for two important extensions