Multi-Dimensional 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 sequential social learning 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 establish a strong discontinuity of learning with respect to the linkage probability. If p is close to but di¤erent from one an arbitrary high proportion of agents select the optimal action in the limit, for any informative signal structure. For bounded signals and a linkage probability equal to one, however, there exists a positive probability that all agents select the suboptimal action. We also show that for every p