Events

Ms. Meichun Lin
Ph.D. Candidate in Management Science
Sauder School of Business
University of British Columbia

ABSTRACT

We consider a sequential search over a group of similar alternatives. The individual value of an alternative contains two components, a utility of a common set of features and an idiosyncratic value. Once an alternative is searched, the feature-based utility can be observed, but the idiosyncratic value remains unknown and needs to be learned by sampling over time. The utilities share an unknown common prior, which captures the similarity across the alternatives and allows for knowledge transfer within the group. The decision maker wants to select an alternative with a high individual value without costing too much in sampling and search. The problem is to decide, sequentially for each alternative, when to stop sampling and whether to accept it or switch to a new one. 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 learning the individual value and the common prior. Moreover, we extend our model and structural results to more practical problems where (i) the sample precision is unknown, (ii) the common prior is shared by the high-dimensional feature vectors rather than the one-dimensional utilities, and (iii) the goal is to select two or more alternatives.