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Maximal Revenue with Multiple Goods: Nonmonotonicity and Other Observations

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  • Sergiu Hart
  • Philip J. Reny

Abstract

Consider the problem of maximizing the revenue from selling a number of goods to a single buyer. We show that, unlike the case of one good, when the buyer's values for the goods increase the seller's maximal revenue may well decrease. We also provide a characterization of revenue-maximizing mechanisms (more generally, of "seller-favorable" mechanisms) that circumvents nondifferentiability issues. Finally, through simple and transparent examples, we clarify the need for and the use of randomization when maximizing revenue in the multiple-goods versus the one-good case.

Suggested Citation

  • Sergiu Hart & Philip J. Reny, 2012. "Maximal Revenue with Multiple Goods: Nonmonotonicity and Other Observations," Discussion Paper Series dp630, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp630
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    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. repec:eee:jetheo:v:172:y:2017:i:c:p:313-347 is not listed on IDEAS
    3. Manelli, Alejandro M. & Vincent, Daniel R., 2012. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly. A corrigendum," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2492-2493.
    4. Menicucci Domenico, 2009. "Competition May Reduce the Revenue in a First Price Auction with Affiliated Private Values," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-19, December.
    5. 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.
    6. Sergiu Hart & Noam Nisan, 2014. "How Good Are Simple Mechanisms for Selling Multiple Goods?," Discussion Paper Series dp666, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    7. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    8. Rochet, J. C., 1985. "The taxation principle and multi-time Hamilton-Jacobi equations," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 113-128, April.
    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. Motty Perry & Philip J. Reny, 1999. "On The Failure of the Linkage Principle in Multi-Unit Auctions," Econometrica, Econometric Society, vol. 67(4), pages 895-900, July.
    11. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-1119, July.
    12. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
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    Cited by:

    1. repec:eee:jetheo:v:172:y:2017:i:c:p:313-347 is not listed on IDEAS
    2. 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.
    3. Tang, Pingzhong & Wang, Zihe, 2017. "Optimal mechanisms with simple menus," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 54-70.
    4. Rochet, Jean-Charles & Thanassoulis, John, 2017. "Intertemporal Price Discrimination with Multiple Products," CEPR Discussion Papers 12034, C.E.P.R. Discussion Papers.
    5. repec:eee:indorg:v:52:y:2017:i:c:p:248-281 is not listed on IDEAS
    6. 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.
    7. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Strategy-proof multi-object auction design: Ex-post revenue maximization with no wastage," ISER Discussion Paper 1001, Institute of Social and Economic Research, Osaka University.
    8. Hafalir, Isa & Miralles, Antonio, 2015. "Welfare-maximizing assignment of agents to hierarchical positions," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 253-270.
    9. repec:eee:matsoc:v:88:y:2017:i:c:p:11-15 is not listed on IDEAS
    10. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.
    11. repec:eee:jetheo:v:173:y:2018:i:c:p:95-117 is not listed on IDEAS
    12. Mishra, Debasis & Pramanik, Anup & Roy, Souvik, 2014. "Multidimensional mechanism design in single peaked type spaces," Journal of Economic Theory, Elsevier, vol. 153(C), pages 103-116.
    13. Ketelaar, Felix & Szalay, Dezso, 2014. "Pricing a Package of Services," CEPR Discussion Papers 10313, C.E.P.R. Discussion Papers.

    More about this item

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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