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Selling to a principal and a budget-constrained agent

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  • Debasis Mishra
  • Kolagani Paramahamsa

Abstract

We analyze a model of selling a single object to a principal-agent pair who want to acquire the object for a firm. The principal and the agent have different assessments of the object's value to the firm. The agent is budget-constrained while the principal is not. The agent participates in the mechanism, but she can (strategically) delegate decision-making to the principal. We derive the revenue-maximizing mechanism in a two-dimensional type space (values of the agent and the principal). We show that below a threshold budget, a mechanism involving two posted prices and three outcomes (one of which involves randomization) is the optimal mechanism for the seller. Otherwise, a single posted price mechanism is optimal.

Suggested Citation

  • Debasis Mishra & Kolagani Paramahamsa, 2022. "Selling to a principal and a budget-constrained agent," Papers 2202.10378, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:2202.10378
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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. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    3. 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.
    4. Geoffroy de Clippel, 2012. "Behavioral Implementation," Working Papers 2012-6, Brown University, Department of Economics.
    5. Bikhchandani, Sushil & Mishra, Debasis, 2022. "Selling two identical objects," Journal of Economic Theory, Elsevier, vol. 200(C).
    6. Yannai A. Gonczarowski & Nicole Immorlica & Yingkai Li & Brendan Lucier, 2021. "Revenue Maximization for Buyers with Costly Participation," Papers 2103.03980, arXiv.org, revised Nov 2023.
    7. Mark Armstrong, 2000. "Optimal Multi-Object Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 455-481.
    8. Che, Yeon-Koo & Gale, Ian, 2000. "The Optimal Mechanism for Selling to a Budget-Constrained Buyer," Journal of Economic Theory, Elsevier, vol. 92(2), pages 198-233, June.
    9. 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.
    10. Baisa, Brian & Rabinovich, Stanislav, 2016. "Optimal auctions with endogenous budgets," Economics Letters, Elsevier, vol. 141(C), pages 162-165.
    11. Li, Yunan, 2021. "Mechanism design with financially constrained agents and costly verification," Theoretical Economics, Econometric Society, vol. 16(3), July.
    12. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    13. Geoffroy de Clippel, 2014. "Behavioral Implementation," American Economic Review, American Economic Association, vol. 104(10), pages 2975-3002, October.
    14. Borgers, Tilman & Krahmer, Daniel & Strausz, Roland, 2015. "An Introduction to the Theory of Mechanism Design," OUP Catalogue, Oxford University Press, number 9780199734023.
    15. 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.
    16. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    17. Andrey Malenko & Anton Tsoy, 2019. "Selling to Advised Buyers," American Economic Review, American Economic Association, vol. 109(4), pages 1323-1348, April.
    18. Burkett, Justin, 2015. "Endogenous budget constraints in auctions," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 1-20.
    19. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    20. Pai, Mallesh M. & Vohra, Rakesh, 2014. "Optimal auctions with financially constrained buyers," Journal of Economic Theory, Elsevier, vol. 150(C), pages 383-425.
    21. Laffont, Jean-Jacques & Robert, Jacques, 1996. "Optimal auction with financially constrained buyers," Economics Letters, Elsevier, vol. 52(2), pages 181-186, August.
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