Competitive algorithms for online pricing

Abstract

Given a seller with m amount of items, a sequence of users {u1, u2, ...} come one by one, the seller must set the unit price and assign some amount of items to each user on his/her arrival. Items can be sold fractionally. Each ui has his/her value function vi (·) such that vi (x) is the highest unit price ui is willing to pay for x items. The objective is to maximize the revenue by setting the price and amount of items for each user. In this paper, we have the following contributions: if the highest value h among all vi (x) is known in advance, we first show the lower bound of the competitive ratio is O(logh), then give an online algorithm with competitive ratio O(logh); if h is not known in advance, we give an online algorithm with competitive ratio O(h3log-1/2h). © 2011 Springer-Verlag.