IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/v11y2011i1n3.html
   My bibliography  Save this article

Optimal Mechanism for Selling Two Goods

Author

Listed:
  • Pavlov Gregory

    (University of Western Ontario, gpavlov@uwo.ca)

Abstract

We solve for the optimal mechanism for selling two goods when the buyer’s demand characteristics are unobservable. In the case of substitutable goods, the seller has an incentive to offer lotteries over goods in order to charge the buyers with large differences in the valuations a higher price for obtaining their desired good with certainty. However, the seller also has a countervailing incentive to make the allocation of the goods among the participating buyers more efficient in order to increase the overall demand. In the case when the buyer can consume both goods, the seller has an incentive to underprovide one of the goods in order to charge the buyers with large valuations a higher price for the bundle of both goods. As in the case of substitutable goods, the seller also has a countervailing incentive to lower the price of the bundle in order to increase the overall demand.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:bejtec:v:11:y:2011:i:1:n:3
    DOI: 10.2202/1935-1704.1664
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1935-1704.1664
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1935-1704.1664?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nicolas Gruyer, 2009. "Optimal Auctions When A Seller Is Bound To Sell To Collusive Bidders," Journal of Industrial Economics, Wiley Blackwell, vol. 57(4), pages 835-850, December.
    2. 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.
    3. Nicolas Gruyer, 2005. "Using lotteries in auctions when buyers collude," Working Papers hal-01021534, HAL.
    4. Nicolas Gruyer, 2005. "Using lotteries in auctions when buyers collude," Economics Working Papers 02, LEEA (air transport economics laboratory), ENAC (french national civil aviation school).
    5. 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.
    6. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    7. Mathias Dewatripont & Lars Peter Hansen & Stephen Turnovsky, 2003. "Advances in economics and econometrics :theory and applications," ULB Institutional Repository 2013/9557, ULB -- Universite Libre de Bruxelles.
    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.
    9. 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.
    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. Guesnerie, Roger & Laffont, Jean-Jacques, 1984. "A complete solution to a class of principal-agent problems with an application to the control of a self-managed firm," Journal of Public Economics, Elsevier, vol. 25(3), pages 329-369, December.
    12. Nicolas Gruyer, 2009. "Optimal auctions when a seller is bound to sell to collusive bidders," Post-Print hal-01021568, HAL.
    13. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
    14. Baron, David P & Myerson, Roger B, 1982. "Regulating a Monopolist with Unknown Costs," Econometrica, Econometric Society, vol. 50(4), pages 911-930, July.
    15. Jean-Charles Rochet & Lars A. Stole, 2002. "Nonlinear Pricing with Random Participation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(1), pages 277-311.
    16. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    17. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    18. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    19. Gregory Pavlov, 2006. "Optimal Mechanism for Selling Substitutes," Boston University - Department of Economics - Working Papers Series WP2006-014, Boston University - Department of Economics.
    20. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Chen, Bo & Ni, Debing, 2017. "Optimal bundle pricing under correlated valuations," International Journal of Industrial Organization, Elsevier, vol. 52(C), pages 248-281.
    4. Bikhchandani, Sushil & Mishra, Debasis, 2022. "Selling two identical objects," Journal of Economic Theory, Elsevier, vol. 200(C).
    5. Briest, Patrick & Chawla, Shuchi & Kleinberg, Robert & Weinberg, S. Matthew, 2015. "Pricing lotteries," Journal of Economic Theory, Elsevier, vol. 156(C), pages 144-174.
    6. Mark Armstrong, 2016. "Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 583-614, October.
    7. Komal Malik & Kolagani Paramahamsa, 2024. "Selling two complementary goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 423-447, June.
    8. Schäfers, Sebastian, 2022. "Product Lotteries and Loss Aversion," Working papers 2022/06, Faculty of Business and Economics - University of Basel.
    9. Chawla, Shuchi & Malec, David & Sivan, Balasubramanian, 2015. "The power of randomness in Bayesian optimal mechanism design," Games and Economic Behavior, Elsevier, vol. 91(C), pages 297-317.
    10. Jean‐Charles Rochet & John Thanassoulis, 2019. "Intertemporal price discrimination with two products," RAND Journal of Economics, RAND Corporation, vol. 50(4), pages 951-973, December.
    11. Mierendorff, Konrad, 2016. "Optimal dynamic mechanism design with deadlines," Journal of Economic Theory, Elsevier, vol. 161(C), pages 190-222.
    12. Carlier, Guillaume & Dupuis, Xavier & Rochet, Jean-Charles & Thanassoulis, John, 2024. "A general solution to the quasi linear screening problem," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    13. Szalay, Dezső & Ketelaar, Felix, 2014. "Pricing a Package of Services," CEPR Discussion Papers 10313, C.E.P.R. Discussion Papers.
    14. Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2024.
    15. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    16. 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.
    17. Jehiel, Philippe & Meyer-ter-Vehn, Moritz & Moldovanu, Benny, 2007. "Mixed bundling auctions," Journal of Economic Theory, Elsevier, vol. 134(1), pages 494-512, May.
    18. 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.
    19. Hanming Fang & Peter Norman, 2006. "To bundle or not to bundle," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 946-963, December.
    20. Ketelaar, Felix & Szalay, Dezsö, 2014. "Pricing a Package of Services - When (not) to bundle," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 487, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.

    More about this item

    Keywords

    multidimensional screening; price discrimination; optimal selling strategies; mechanism design;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:bejtec:v:11:y:2011:i:1:n:3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.