COMPETITIVE ALGORITHMS FOR ONLINE PRICING
Yong Zhang, Yuxin Wang, Francis Y. L. Chin, Hing‐Fung Ting · Discrete Mathematics Algorithms and Applications · 2012
Given a seller with m items, a sequence of users {u1, u2, …} come one by one, the seller must set the unit price and assign some 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 number 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 ⌊ log h⌋/2, then give an online algorithm with competitive ratio 4⌊ log h⌋ + 6; if h is not known in advance, we give an online algorithm with competitive ratio 2⋅h log -1/2 h + 8⋅h3 log -1/2 h.