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—Optimal Mechanism for Selling a Set of Commonly Ranked Objects

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  • Juan Feng

    (Warrington College of Business Administration, University of Florida, Gainesville, Florida)

Abstract

This paper designs an optimal mechanism for selling a set of commonly ranked objects. Although buyers rank these objects in the same order, the rates at which their valuations change for a less-preferred object might be different. Four stylized cases are identified according to this difference: parallel, convergent, divergent, and convergent-then-divergent. In general, the optimal mechanism cannot be interpreted as a conventional second-price auction. A reserve price is imposed for each object. Depending on which of the four stylized cases is considered, a higher-value bidder may be allocated a higher-ranked or lower-ranked object. There is also a positive probability that a higher-ranked object is not allocated while a lower-ranked one allocated. In a departure from the extant mechanism-design literature, the individual-rationality constraint for a mid-range type of bidder can be binding.

Suggested Citation

  • Juan Feng, 2008. "—Optimal Mechanism for Selling a Set of Commonly Ranked Objects," Marketing Science, INFORMS, vol. 27(3), pages 501-512, 05-06.
    • Handle: RePEc:inm:ormksc:v:27:y:2008:i:3:p:501-512
    DOI: 10.1287/mksc.1070.0290
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    References listed on IDEAS

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    8. Estrella Alonso & Joaquin Sanchez-Soriano & Juan Tejada, 2015. "A parametric family of two ranked objects auctions: equilibria and associated risk," Annals of Operations Research, Springer, vol. 225(1), pages 141-160, February.
    9. Xiaoquan (Michael) Zhang & Juan Feng, 2011. "Cyclical Bid Adjustments in Search-Engine Advertising," Management Science, INFORMS, vol. 57(9), pages 1703-1719, February.
    10. Carsten D. Schultz, 2020. "The impact of ad positioning in search engine advertising: a multifaceted decision problem," Electronic Commerce Research, Springer, vol. 20(4), pages 945-968, December.
    11. Scott Fay & Juliano Laran, 2009. "Implications of Expected Changes in the Seller's Price in Name-Your-Own-Price Auctions," Management Science, INFORMS, vol. 55(11), pages 1783-1796, November.
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    13. Estrella Alonso & Joaquín Sánchez-Soriano & Juan Tejada, 2020. "Mixed Mechanisms for Auctioning Ranked Items," Mathematics, MDPI, vol. 8(12), pages 1-26, December.

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