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Robustly Optimal Mechanisms for Selling Multiple Goods

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  • Yeon-Koo Che
  • Weijie Zhong

Abstract

We study robustly optimal mechanisms for selling multiple items. The seller maximizes revenue against a worst-case distribution of a buyer's valuations within a set of distributions, called an "ambiguity" set. We identify the exact forms of robustly optimal selling mechanisms and the worst-case distributions when the ambiguity set satisfies various moment conditions on the values of subsets of goods. The analysis reveals general properties of the ambiguity set that justifies categorical bundling, which includes separate sales and pure bundling as special cases.

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  • Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2024.
    • Handle: RePEc:arx:papers:2105.02828
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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. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    4. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    5. Constantinos Daskalakis & Alan Deckelbaum & Christos Tzamos, 2017. "Strong Duality for a Multiple‐Good Monopolist," Econometrica, Econometric Society, vol. 85, pages 735-767, May.
    6. Anne-Katrin Roesler & Balázs Szentes, 2017. "Buyer-Optimal Learning and Monopoly Pricing," American Economic Review, American Economic Association, vol. 107(7), pages 2072-2080, July.
    7. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2016. "Informationally Robust Optimal Auction Design," Working Papers 084_2016, Princeton University, Department of Economics, Econometric Research Program..
    8. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2019. "Revenue Guarantee Equivalence," American Economic Review, American Economic Association, vol. 109(5), pages 1911-1929, May.
    9. Menicucci, Domenico & Hurkens, Sjaak & Jeon, Doh-Shin, 2015. "On the optimality of pure bundling for a monopolist," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 33-42.
    10. 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.
    11. Songzi Du, 2018. "Robust Mechanisms Under Common Valuation," Econometrica, Econometric Society, vol. 86(5), pages 1569-1588, September.
    12. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    13. Dirk Bergemann & Karl H. Schlag, 2012. "Pricing Without Priors," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 12, pages 405-415, World Scientific Publishing Co. Pte. Ltd..
    14. Manelli, Alejandro M. & Vincent, Daniel R., 2006. "Bundling as an optimal selling mechanism for a multiple-good monopolist," Journal of Economic Theory, Elsevier, vol. 127(1), pages 1-35, March.
    15. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    16. Gabriel Carroll, 2015. "Robustness and Linear Contracts," American Economic Review, American Economic Association, vol. 105(2), pages 536-563, February.
    17. , & , J., 2015. "Maximal revenue with multiple goods: nonmonotonicity and other observations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    18. Carrasco, Vinicius & Farinha Luz, Vitor & Kos, Nenad & Messner, Matthias & Monteiro, Paulo & Moreira, Humberto, 2018. "Optimal selling mechanisms under moment conditions," Journal of Economic Theory, Elsevier, vol. 177(C), pages 245-279.
    19. 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.
    20. Carroll, Gabriel, 2019. "Robust incentives for information acquisition," Journal of Economic Theory, Elsevier, vol. 181(C), pages 382-420.
    21. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    22. Doron Ravid & Anne-Katrin Roesler & Balázs Szentes, 2022. "Learning before Trading: On the Inefficiency of Ignoring Free Information," Journal of Political Economy, University of Chicago Press, vol. 130(2), pages 346-387.
    23. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    24. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    25. William James Adams & Janet L. Yellen, 1976. "Commodity Bundling and the Burden of Monopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(3), pages 475-498.
    26. Mark Armstrong, 1999. "Price Discrimination by a Many-Product Firm," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 151-168.
    27. Yingni Guo & Eran Shmaya, 2019. "Robust Monopoly Regulation," Papers 1910.04260, arXiv.org.
    28. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
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    Cited by:

    1. Jerry Anunrojwong & Santiago R. Balseiro & Omar Besbes, 2022. "On the Robustness of Second-Price Auctions in Prior-Independent Mechanism Design," Papers 2204.10478, arXiv.org, revised Jan 2024.

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