Abstract
Given a seller with m amount of items, a sequence of users {u 1, u 2, ...} 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 u i has his/her value function v i (·) such that v i (x) is the highest unit price u i 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 v i (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 \(O(h^{3\log^{-1/2}h})\).
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Zhang, Y., Chin, F.Y.L., Ting, HF. (2011). Competitive Algorithms for Online Pricing. In: Fu, B., Du, DZ. (eds) Computing and Combinatorics. COCOON 2011. Lecture Notes in Computer Science, vol 6842. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22685-4_35
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DOI: https://doi.org/10.1007/978-3-642-22685-4_35
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