Online pricing for bundles of multiple items

Yong Zhang (), Francis Chin () and Hing-Fung Ting ()

Journal of Global Optimization, 2014, vol. 58, issue 2, 377-387

Abstract: Given a seller with $$k$$ types of items, $$m$$ of each, a sequence of users $$\{u_1, u_2,\ldots \}$$ arrive one by one. Each user is single-minded, i.e., each user is interested only in a particular bundle of items. The seller must set the price and assign some amount of bundles to each user upon his/her arrival. Bundles can be sold fractionally. Each $$u_i$$ has his/her value function $$v_i(\cdot )$$ such that $$v_i(x)$$ is the highest unit price $$u_i$$ is willing to pay for $$x$$ bundles. The objective is to maximize the revenue of the seller by setting the price and amount of bundles for each user. In this paper, we first show that a lower bound of the competitive ratio for this problem is $$\Omega (\log h+\log k)$$ , where $$h$$ is the highest unit price to be paid among all users. We then give a deterministic online algorithm, Pricing, whose competitive ratio is $$O(\sqrt{k}\cdot \log h\log k)$$ . When $$k=1$$ the lower and upper bounds asymptotically match the optimal result $$O(\log h)$$ . Copyright Springer Science+Business Media New York 2014

Keywords: Online algorithms; Pricing; Competitive ratio (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10898-013-0043-4

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