Optimal adaptive price search
Consider the problem of a consumer desiring to buy a good which is sold at a variety of prices. Such a buyer will be able to obtain a sequence of price quotations from various sellers. When should the buyer stop searching for a lower price? If he continues, he may obtain a lower price, but he incurs additional time, effort and expense in searching. The optimal price search decision is one of balancing the expectation of a possibly lower price obtained by continued search against cumulative costs from search. When the prices arise from a known probability distribution, the optimal search strategy has certain well-defined and desirable properties. In the more realistic case that the buyer has only partial information about the price distribution and must update his beliefs after observing prices in the marketplace, the problem becomes more complex, and search strategies become less well behaved. The major purpose of this article is to determine new conditions under which optimal policies have these desirable characteristics in the case where the consumer possesses only incomplete information about the distribution of prices. Price quotations he receives, in addition to providing him with price possibilities, provide him with information about that distribution. Rothschild [ 151, in citing an unpublished paper of Gastwirth, has noted that small specification errors for an assumed distribution can lead to substantial changes in expected number of searches and expected cost. Consequently, the assumption of a known distribution of prices can have a profound effect on total cost. 1 0022-053 l/8 l/040001-20$02.00/O