IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/v11y2011i1n4.html
   My bibliography  Save this article

A Property of Solutions to Linear Monopoly Problems

Author

Listed:
  • Pavlov Gregory

    (University of Western Ontario)

Abstract

We extend the “no-haggling” result of Riley and Zeckhauser (1983) to the class of linear multiproduct monopoly problems when the buyer’s valuations are smoothly distributed. In particular, we show that there is no loss for the seller in optimizing over mechanisms such that all allocations belong to the boundary of the feasible set. The set of potentially optimal mechanisms can be further restricted when the costs are sufficiently low: the optimal mechanisms use only allocations from the “north-east” boundary of the feasible set and the null allocation.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:bejtec:v:11:y:2011:i:1:n:4
    DOI: 10.2202/1935-1704.1663
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1935-1704.1663
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1935-1704.1663?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. 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. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(5), pages 687-698, October.
    3. Nicolas Gruyer, 2009. "Optimal auctions when a seller is bound to sell to collusive bidders," Post-Print hal-01021568, HAL.
    4. 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.
    5. Baron, David P & Myerson, Roger B, 1982. "Regulating a Monopolist with Unknown Costs," Econometrica, Econometric Society, vol. 50(4), pages 911-930, July.
    6. 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.
    7. 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.
    8. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(3), pages 381-386, June.
    9. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(4), pages 525-537, August.
    10. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
    11. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(2), pages 285-292, April.
    12. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    13. ,, 1998. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 14(1), pages 151-159, February.
    14. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    15. Nicolas Gruyer, 2005. "Using lotteries in auctions when buyers collude," Working Papers hal-01021534, HAL.
    16. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    17. 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).
    18. 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.
    19. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    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.
    21. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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. Dirk Bergemann & Marco Ottaviani, 2021. "Information Markets and Nonmarkets," Cowles Foundation Discussion Papers 2296, Cowles Foundation for Research in Economics, Yale University.
    3. 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.
    4. Bikhchandani, Sushil & Mishra, Debasis, 2022. "Selling two identical objects," Journal of Economic Theory, Elsevier, vol. 200(C).
    5. Schäfers, Sebastian, 2022. "Product Lotteries and Loss Aversion," Working papers 2022/06, Faculty of Business and Economics - University of Basel.
    6. Chen, Xi & Diakonikolas, Ilias & Paparas, Dimitris & Sun, Xiaorui & Yannakakis, Mihalis, 2018. "The complexity of optimal multidimensional pricing for a unit-demand buyer," Games and Economic Behavior, Elsevier, vol. 110(C), pages 139-164.
    7. Briest, Patrick & Chawla, Shuchi & Kleinberg, Robert & Weinberg, S. Matthew, 2015. "Pricing lotteries," Journal of Economic Theory, Elsevier, vol. 156(C), pages 144-174.
    8. Tang, Pingzhong & Wang, Zihe, 2017. "Optimal mechanisms with simple menus," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 54-70.
    9. Komal Malik & Kolagani Paramahamsa, 2020. "Selling two complementary goods," Papers 2011.05840, arXiv.org, revised Jul 2022.
    10. Komal Malik & Kolagani Paramahamsa, 2021. "Selling two complementary goods," Discussion Papers 21-01, Indian Statistical Institute, Delhi.

    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. "Optimal Mechanism for Selling Two Goods," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-35, 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. Mark Armstrong, 2016. "Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 583-614, October.
    5. Bikhchandani, Sushil & Mishra, Debasis, 2022. "Selling two identical objects," Journal of Economic Theory, Elsevier, vol. 200(C).
    6. Briest, Patrick & Chawla, Shuchi & Kleinberg, Robert & Weinberg, S. Matthew, 2015. "Pricing lotteries," Journal of Economic Theory, Elsevier, vol. 156(C), pages 144-174.
    7. 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.
    8. Yeon-Koo Che & Weijie Zhong, 2021. "Robustly Optimal Mechanisms for Selling Multiple Goods," Papers 2105.02828, arXiv.org, revised Aug 2022.
    9. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    10. 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.
    11. Schäfers, Sebastian, 2022. "Product Lotteries and Loss Aversion," Working papers 2022/06, Faculty of Business and Economics - University of Basel.
    12. Mierendorff, Konrad, 2016. "Optimal dynamic mechanism design with deadlines," Journal of Economic Theory, Elsevier, vol. 161(C), pages 190-222.
    13. Jehiel, Philippe & Meyer-ter-Vehn, Moritz & Moldovanu, Benny, 2007. "Mixed bundling auctions," Journal of Economic Theory, Elsevier, vol. 134(1), pages 494-512, May.
    14. Szalay, Dezső & Ketelaar, Felix, 2014. "Pricing a Package of Services," CEPR Discussion Papers 10313, C.E.P.R. Discussion Papers.
    15. Sergiu Hart & Noam Nisan, 2013. "Selling Multiple Correlated Goods: Revenue Maximization and Menu-Size Complexity (old title: "The Menu-Size Complexity of Auctions")," Papers 1304.6116, arXiv.org, revised Nov 2018.
    16. Hart, Sergiu & Nisan, Noam, 2019. "Selling multiple correlated goods: Revenue maximization and menu-size complexity," Journal of Economic Theory, Elsevier, vol. 183(C), pages 991-1029.
    17. 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.
    18. Hanming Fang & Peter Norman, 2006. "To bundle or not to bundle," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 946-963, December.
    19. 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.
    20. 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.

    More about this item

    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:4. 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.