Optimal Design of Online Sequential Buy-Price Auctions with Consumer Valuation Learning

Buy-price auction has been successfully used as a new channel of online sales. This paper studies an online sequential buy-price auction problem, where a seller has an inventory of identical products and needs to clear them through a sequence of online buy-price auctions such that the total profit is maximized by optimizing the buy price in each auction. We propose a methodology by dynamic programming approach to solve this optimization problem. Since the consumers’ behavior affects the seller’s revenue, the consumers’ strategy used in this auction is first investigated. Then, two different dynamic programming models are developed to optimize the seller’s decision-making: one is the clairvoyant model corresponding to a situation where the seller has complete information about consumer valuations, and the other is the Bayesian learning model where the seller makes optimal decisions by continuously recording and utilizing auction data during the sales process. Numerical experiments are employed to demonstrate the impacts of several key factors on the optimal solutions, including the size of inventory, the number of potential consumers, and the rate at which the seller discounts early incomes. It is shown that when the consumers’ valuations are uniformly distributed, the Bayesian learning model is of great efficiency if the demand is adequate.