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Maximal revenue with multiple goods: nonmonotonicity and other observations

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  • ,

    (Departments of Economics, Department of Mathematics and The Federmann Center for the study of Rationality, The Hebrew University of Jerusalem)

  • , J.

    (Department of Economics, University of Chicago)

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 then identify two circumstances where monotonicity does obtain: when optimal mechanisms are deterministic and symmetric, and when they have submodular prices. Next, through simple and transparent examples, we clarify the need for and the advantage of randomization when maximizing revenue in the multiple-good versus the one-good case. Finally, we consider "seller-favorable" mechanisms, the only ones that matter when maximizing revenue. They are essential for our positive monotonicity results, and they also circumvent well-known nondifferentiability issues.

Suggested Citation

  • , & , J., 2015. "Maximal revenue with multiple goods: nonmonotonicity and other observations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    • Handle: RePEc:the:publsh:1517
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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.
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    More about this item

    Keywords

    Revenue maximization; multidimensional types; nonmonotonicity; randomization; differentiability;
    All these keywords.

    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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