Uncertain Search with Knowledge Transfer

We consider a sequential search over a group of similar alternatives. The individual value of an alternative contains two components: an observable utility and an idiosyncratic value. Observable utilities share an unknown population distribution, which captures the similarity across the alternatives and allows for knowledge transfer within the group. Once a decision maker encounters an alternative, its utility is revealed immediately, whereas the idiosyncratic value is unobservable and needs to be learned by sampling. The goal is to select an alternative with the highest individual value, accounting for the sampling and search costs. A novel feature of this problem is the combination of the individual and population levels of learning. We formulate the problem as a Bayesian dynamic program and characterize the optimal policy by a threshold structure. We show that it depends on the difference between the mean estimates of the current alternative and the population. It is optimal to continue sampling if the difference is between a threshold pair; otherwise, accept the current alternative if it exceeds the upper threshold, and switch to a new one if it is below the lower threshold. Other structural properties are also derived to shed light on the effects of the two levels of learning. A key insight is that more uncertainty is preferable at the individual level, but less uncertainty is preferable at the population level. Various practical variants of the problem are also considered.