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Bundling Complements

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  • Weijie Zhong

Abstract

I develop a duality-based multi-dimensional screening framework with a geometric characterization of combinatorial preferences. For a mechanism to be optimal, the type distribution pins down \emph{required} directions of binding feasibility constraints, while the complementarity among bundles determines the \emph{covered} directions; optimality reduces to full coverage of required directions. I apply the framework to a one-parameter family in which every bundle containing a fixed \emph{core} of items earns a complementarity premium. Two thresholds organize the optimum: above a lower threshold the grand bundle must be offered; above a higher threshold a \emph{core-peripheral} menu -- a bundled core with optional add-ons that are not sold standalone -- is optimal. The tight distributional condition for finiteness of the higher threshold is \emph{inclusivity}, that the menu exclude no near-top buyer.

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  • Weijie Zhong, 2026. "Bundling Complements," Papers 2607.07982, arXiv.org.
    • Handle: RePEc:arx:papers:2607.07982
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    References listed on IDEAS

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    1. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    2. Andreas Kleiner & Alejandro Manelli, 2019. "Strong Duality in Monopoly Pricing," Econometrica, Econometric Society, vol. 87(4), pages 1391-1396, July.
    3. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    4. Constantinos Daskalakis & Alan Deckelbaum & Christos Tzamos, 2017. "Strong Duality for a Multiple‐Good Monopolist," Econometrica, Econometric Society, vol. 85, pages 735-767, May.
    5. Nima Haghpanah & Jason Hartline, 2021. "When Is Pure Bundling Optimal?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(3), pages 1127-1156.
    6. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    7. 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.
    8. Mira Frick & Ryota Iijima & Yuhta Ishii, 2026. "Multidimensional Screening With Precise Seller Information," Econometrica, Econometric Society, vol. 94(1), pages 35-70, January.
    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. Bikhchandani, Sushil & Mishra, Debasis, 2024. "Rank-preserving multidimensional mechanisms: An equivalence between identical-object and heterogeneous-object models," Journal of Economic Theory, Elsevier, vol. 222(C).
    11. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
    12. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
    13. 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.
    14. , & , J., 2015. "Maximal revenue with multiple goods: nonmonotonicity and other observations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    15. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
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