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Online pricing for bundles of multiple items

Author

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  • Yong Zhang
  • Francis Chin
  • Hing-Fung Ting

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

Suggested Citation

  • Yong Zhang & Francis Chin & Hing-Fung Ting, 2014. "Online pricing for bundles of multiple items," Journal of Global Optimization, Springer, vol. 58(2), pages 377-387, February.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:2:p:377-387
    DOI: 10.1007/s10898-013-0043-4
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    References listed on IDEAS

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    1. Grigoriev, A. & van Loon, J. & Uetz, M.J. & Sitters, R., 2006. "How to sell a graph: guidelines for graph retailers," Research Memorandum 001, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
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    Cited by:

    1. Weisstein, Fei L. & Song, Lei & Andersen, Peter & Zhu, Ying, 2017. "Examining impacts of negative reviews and purchase goals on consumer purchase decision," Journal of Retailing and Consumer Services, Elsevier, vol. 39(C), pages 201-207.
    2. Li, Jianbin & Liu, Lang & Luo, Xiaomeng & Zhu, Stuart X., 2023. "Interactive bundle pricing strategy for online pharmacies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).

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