An empirical bayes solution to the best–choice problem

Abstract

We consider the problem of a consumer desiring to buy an item at as low a price as possible based on a finite sequence of price quotations obtained sequentially from various sellers. This is a version of the so-called best-choice problem. It is assumed that the optimal decision is concerned with the probability-maximizing approach. When the distribution of price quotations is completely known, the optimal buying policy is myopic. Many authors have shown that the myopic policy is still optimal in some cases where the price distribution has unknown parameter(s) and the buyer's prior on this parameter undergoes Bayesian updating as successive prices are received. In this article, we examine the case in which the buyer must update his/her beliefs in a Bayesian manner, but the prior distribution is not completely known to the buyer. We assume, however, that some auxiliary information is available to the buyer. Using empirical Bayes techniques, a stopping time for the price search is constructed for such situations