Competitive algorithms for online pricing

Authors:
Yong Zhang;Francis Y. L. Chin;Hing-Fung Ting
Affiliations:
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, China and Department of Computer Science, The University of Hong Kong, Hong Kong;Department of Computer Science, The University of Hong Kong, Hong Kong;Department of Computer Science, The University of Hong Kong, Hong Kong
Venue:
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Year:
2011

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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(ċ) 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(log h), then give an online algorithm with competitive ratio O(log h); if h is not known in advance, we give an online algorithm with competitive ratio O(h3 log -1/2 h).