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Matroid prophet inequalities and applications to multi-dimensional mechanism design

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  • Kleinberg, Robert
  • Weinberg, S. Matthew

Abstract

Consider a gambler who observes a sequence of independent random numbers and is allowed to stop at any time, claiming reward equal to the most recent observation. The famous prophet inequality of Krengel, Sucheston, and Garling asserts that a gambler who knows the distribution of each random variable can achieve half as much reward, in expectation, as a “prophet” who knows the sampled values and can choose the largest one. We generalize this result to settings in which the gambler and the prophet are allowed to make multiple selections, subject to a matroid constraint, showing that the gambler can still achieve half as much reward as the prophet.

Suggested Citation

  • Kleinberg, Robert & Weinberg, S. Matthew, 2019. "Matroid prophet inequalities and applications to multi-dimensional mechanism design," Games and Economic Behavior, Elsevier, vol. 113(C), pages 97-115.
    • Handle: RePEc:eee:gamebe:v:113:y:2019:i:c:p:97-115
    DOI: 10.1016/j.geb.2014.11.002
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    References listed on IDEAS

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    1. Jason D. Hartline, 2012. "Approximation in Mechanism Design," American Economic Review, American Economic Association, vol. 102(3), pages 330-336, May.
    2. 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.
    3. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    4. Kennedy, D. P., 1987. "Prophet-type inequalities for multi-choice optimal stopping," Stochastic Processes and their Applications, Elsevier, vol. 24(1), pages 77-88, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Multi-dimensional mechanism design; Auction theory; Revenue; Online optimization; Stochastic optimization;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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