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 decides 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 willing to pay does not change over time. The question then is how should the seller 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 opportunity to make a profit. In particular, we provide a polynomial-time algorithm that finds a:pricing algorithm (strategy) for the seller that minimizes the average (total) losses over time, Further, we provide efficient algorithms for finding pricing strategies for maximizing the cumulative seller's profits when the sales period is limited, there is a limited supply of the product for sale, and the buyer's valuation is a non-increasing function of time, where those functions are known to the seller. We also present preliminary results on pricing strategies that minimize the maximum loss, and we show show that there is no strategy minimizing both the total loss and the maximum loss at the same time. (C) 2000 Elsevier Science Inc. All rights reserved.