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Selling two complementary goods

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  • Komal Malik
  • Kolagani Paramahamsa

Abstract

A seller is selling a pair of divisible complementary goods to an agent. The agent consumes the goods only in a specific ratio and freely disposes of excess in either goods. The value of the bundle and the ratio are private information of the agent. In this two-dimensional type space model, we characterize the incentive constraints and show that the optimal (expected revenue-maximizing) mechanism is a ratio-dependent posted price or a posted price mechanism for a class of distributions. We also show that the optimal mechanism is a posted price mechanism when the value and the ratio are independently distributed.

Suggested Citation

  • Komal Malik & Kolagani Paramahamsa, 2020. "Selling two complementary goods," Papers 2011.05840, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:2011.05840
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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. 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.
    3. , & , J., 2015. "Maximal revenue with multiple goods: nonmonotonicity and other observations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    4. 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.
    5. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    6. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    7. Devanur, Nikhil R. & Haghpanah, Nima & Psomas, Alexandros, 2020. "Optimal multi-unit mechanisms with private demands," Games and Economic Behavior, Elsevier, vol. 121(C), pages 482-505.
    8. 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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