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A Constructive Characterization of Optimal Bundling

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  • Zhiming Feng

Abstract

This paper studies a monopolist selling multiple goods to a consumer with one-dimensional private types. I provide a sufficient condition under which the monopolist's problem is equivalent to finding the upper envelope of the marginal revenue curves. This approach guarantees that the optimal mechanism is deterministic and can be implemented via a menu of bundles. I further characterize this upper envelope using a dominance notion. This characterization yields a constructive algorithm to compute the optimal menu by iteratively eliminating dominated bundles. As my main application, I use this framework to introduce and provide sufficient conditions for the optimality of tree bundling, a common but previously unmodeled sales strategy where the optimal menu contains a root bundle but features distinct upgrade paths.

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  • Zhiming Feng, 2025. "A Constructive Characterization of Optimal Bundling," Papers 2502.07863, arXiv.org, revised Sep 2025.
    • Handle: RePEc:arx:papers:2502.07863
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    References listed on IDEAS

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    1. Constantinos Daskalakis & Alan Deckelbaum & Christos Tzamos, 2017. "Strong Duality for a Multiple‐Good Monopolist," Econometrica, Econometric Society, vol. 85, pages 735-767, May.
    2. Nima Haghpanah & Jason Hartline, 2021. "When Is Pure Bundling Optimal? [Commodity Bundling and the Burden of Monopoly]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(3), pages 1127-1156.
    3. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    4. Manelli, Alejandro M. & Vincent, Daniel R., 2012. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly. A corrigendum," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2492-2493.
    5. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    6. Toikka, Juuso, 2011. "Ironing without control," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2510-2526.
    7. Laffont, Jean-Jacques & Tirole, Jean, 1986. "Using Cost Observation to Regulate Firms," Journal of Political Economy, University of Chicago Press, vol. 94(3), pages 614-641, June.
    8. Soheil Ghili, 2023. "A Characterization for Optimal Bundling of Products with Nonadditive Values," American Economic Review: Insights, American Economic Association, vol. 5(3), pages 311-326, September.
    9. 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.
    10. R. Preston McAfee & John McMillan & Michael D. Whinston, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 371-383.
    11. 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.
    12. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    13. Jullien, Bruno, 2000. "Participation Constraints in Adverse Selection Models," Journal of Economic Theory, Elsevier, vol. 93(1), pages 1-47, July.
    14. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    15. 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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