Strategies for maximizing seller's profit under unknown buyer's valuations

Suppose there is a seller that has an unlimited number of units of a-single product for sale. The seller at each moment of time posts a price for his/ her product. Based on the posted pricer at each moment of time, a buyer dec ides whether or not to buy a unit of that product from the seller. The only information about the buyer available to the seller is,the seller's sales history. Further, we assume that the maximal unit price the buyer is willin g to pay does not change over time. The question then is how should the sel ler price his/her product to maximize profits? To address this question, we use the notion of loss functions. Intuitively, a loss function is a measure, at each moment of time, of the lost opportun ity to make a profit. In particular, we provide a polynomial-time algorithm that finds a:pricing algorithm (strategy) for the seller that minimizes th e average (total) losses over time, Further, we provide efficient algorithm s for finding pricing strategies for maximizing the cumulative seller's pro fits when the sales period is limited, there is a limited supply of the pro duct for sale, and the buyer's valuation is a non-increasing function of ti me, where those functions are known to the seller. We also present prelimin ary results on pricing strategies that minimize the maximum loss, and we sh ow show that there is no strategy minimizing both the total loss and the ma ximum loss at the same time. (C) 2000 Elsevier Science Inc. All rights rese rved.