Abstract
We consider a monopoly pricing problem, where a seller has multiple items to sell to a single buyer, only knowing the distribution of the buyer’s value profile. The seller’s goal is to maximize her expected revenue. In general, this is a difficult problem to solve, even if the distribution is well specified. In this paper, we solve a subclass of this problem when the distribution is assumed to belong to the class of distributions defined by given marginal partial information. Under this model, we show that the optimal strategy for the seller is a randomized posted price mechanism under which the items are sold separately, and the result continues to hold even when the buyer has a budget feasibility constraint. Consequently, under some specific ambiguity sets which include moment-based and Wasserstein ambiguity sets, we provide analytical solutions for these single-item problems. Based on the additive separation property, we show the general additive separation problem is a special case of resource allocation problems that can be solved by known polynomial-time algorithms.
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Acknowledgements
Zhen Wang received support from the National Science Foundation of China (NSFC) Grant 72301235, the Guangdong Key Lab of Mathematical Foundations for Artificial Intelligence and the Shenzhen Science and Technology Program under Grant ZDSYS20220606100601002. Simai He received support from the Major Program of National Natural Science Foundation of China (NSFC) Grant (72192830,72192832) and Grant 71825003. The authors thank the senior editor, the associate editor, and the three reviewers for constructive comments on the previous drafts of this paper.
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Qiu, H., Wang, Z., He, S. (2024). Separation in Distributionally Robust Monopolist Problem. In: Garg, J., Klimm, M., Kong, Y. (eds) Web and Internet Economics. WINE 2023. Lecture Notes in Computer Science, vol 14413. Springer, Cham. https://doi.org/10.1007/978-3-031-48974-7_31
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