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The complexity of optimal multidimensional pricing for a unit-demand buyer

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  • Chen, Xi
  • Diakonikolas, Ilias
  • Paparas, Dimitris
  • Sun, Xiaorui
  • Yannakakis, Mihalis

Abstract

We resolve the complexity of revenue-optimal deterministic auctions in the unit-demand single-buyer Bayesian setting, i.e., the optimal item pricing problem, when the buyer's values for the items are independent. We show that the problem of computing a revenue-optimal pricing can be solved in polynomial time for distributions of support size 2, and its decision version is NP-complete for distributions of support size 3. We also show that the problem remains NP-complete for the case of identical distributions.

Suggested Citation

  • Chen, Xi & Diakonikolas, Ilias & Paparas, Dimitris & Sun, Xiaorui & Yannakakis, Mihalis, 2018. "The complexity of optimal multidimensional pricing for a unit-demand buyer," Games and Economic Behavior, Elsevier, vol. 110(C), pages 139-164.
  • Handle: RePEc:eee:gamebe:v:110:y:2018:i:c:p:139-164
    DOI: 10.1016/j.geb.2018.03.016
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    References listed on IDEAS

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    1. Sergiu Hart & Noam Nisan, 2013. "The Menu-Size Complexity of Auctions," Discussion Paper Series dp637, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    3. Chawla, Shuchi & Malec, David & Sivan, Balasubramanian, 2015. "The power of randomness in Bayesian optimal mechanism design," Games and Economic Behavior, Elsevier, vol. 91(C), pages 297-317.
    4. Manelli, Alejandro M. & Vincent, Daniel R., 2007. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly," Journal of Economic Theory, Elsevier, vol. 137(1), pages 153-185, November.
    5. Pavlov Gregory, 2011. "A Property of Solutions to Linear Monopoly Problems," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-18, February.
    6. Shuchi Chawla & Jason Hartline & David Malec & Balasubramanian Sivan, 2010. "Sequential Posted Pricing and Multi-parameter Mechanism Design," Discussion Papers 1486, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    8. Tang, Pingzhong & Wang, Zihe, 2017. "Optimal mechanisms with simple menus," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 54-70.
    9. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
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    Cited by:

    1. Moshe Babaioff & Michal Feldman & Yannai A. Gonczarowski & Brendan Lucier & Inbal Talgam-Cohen, 2020. "Escaping Cannibalization? Correlation-Robust Pricing for a Unit-Demand Buyer," Papers 2003.05913, arXiv.org, revised Aug 2020.
    2. Adam N. Elmachtoub & Michael L. Hamilton, 2021. "The Power of Opaque Products in Pricing," Management Science, INFORMS, vol. 67(8), pages 4686-4702, August.
    3. Zhenzhen Yan & Karthik Natarajan & Chung Piaw Teo & Cong Cheng, 2022. "A Representative Consumer Model in Data-Driven Multiproduct Pricing Optimization," Management Science, INFORMS, vol. 68(8), pages 5798-5827, August.

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