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A Simple and Approximately Optimal Mechanism for a Buyer with Complements

Author

Listed:
  • Alon Eden

    (Computer Science Department, Harvard University, Cambridge, Massachusetts 02139, Simons Institute for the Theory of Computing, Berkeley, California 94720)

  • Michal Feldman

    (Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 6997801, Israel, Microsoft Research, Herzliya 4672513, Israel)

  • Ophir Friedler

    (Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 6997801, Israel)

  • Inbal Talgam-Cohen

    (Computer Science Department, Technion, Haifa 3200003, Israel)

  • S. Matthew Weinberg

    (Simons Institute for the Theory of Computing, Berkeley, California 94720, Computer Science Department, Princeton University, Princeton, New Jersey 08540)

Abstract

We consider a revenue-maximizing seller with m heterogeneous items and a single buyer whose valuation for the items may exhibit both substitutes and complements. We show that the better of selling the items separately and bundling them together— guarantees a Θ ( d ) -fraction of the optimal revenue, where d is a measure of the degree of complementarity; it extends prior work showing that the same simple mechanism achieves a constant-factor approximation when buyer valuations are subadditive (the most general class of complement-free valuations). Our proof is enabled by a recent duality framework, which we use to obtain a bound on the optimal revenue in the generalized setting. Our technical contributions are domain specific to handle the intricacies of settings with complements. One key modeling contribution is a tractable notion of “degree of complementarity” that admits meaningful results and insights—we demonstrate that previous definitions fall short in this regard.

Suggested Citation

  • Alon Eden & Michal Feldman & Ophir Friedler & Inbal Talgam-Cohen & S. Matthew Weinberg, 2021. "A Simple and Approximately Optimal Mechanism for a Buyer with Complements," Operations Research, INFORMS, vol. 69(1), pages 188-206, January.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:1:p:188-206
    DOI: 10.1287/opre.2020.2039
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    References listed on IDEAS

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    1. Pavlov Gregory, 2011. "Optimal Mechanism for Selling Two Goods," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-35, February.
    2. 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.
    3. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    4. 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.
    5. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    6. John Riley & Richard Zeckhauser, 1983. "Optimal Selling Strategies: When to Haggle, When to Hold Firm," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(2), pages 267-289.
    7. Shahar Dobzinski & Noam Nisan & Michael Schapira, 2010. "Approximation Algorithms for Combinatorial Auctions with Complement-Free Bidders," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 1-13, February.
    8. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    9. , & , J., 2015. "Maximal revenue with multiple goods: nonmonotonicity and other observations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    10. Levin, Jonathan, 1997. "An Optimal Auction for Complements," Games and Economic Behavior, Elsevier, vol. 18(2), pages 176-192, February.
    11. 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.
    12. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    13. Nisan, Noam & Segal, Ilya, 2006. "The communication requirements of efficient allocations and supporting prices," Journal of Economic Theory, Elsevier, vol. 129(1), pages 192-224, July.
    14. Jason D. Hartline & Brendan Lucier, 2015. "Non-optimal Mechanism Design," American Economic Review, American Economic Association, vol. 105(10), pages 3102-3124, October.
    15. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
    16. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 393-407, March.
    17. Paul Milgrom, 2007. "Package Auctions and Exchanges," Econometrica, Econometric Society, vol. 75(4), pages 935-965, July.
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    Cited by:

    1. Shixin Wang, 2023. "The Power of Simple Menus in Robust Selling Mechanisms," Papers 2310.17392, arXiv.org, revised Sep 2024.

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