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Ranking asymmetric auctions: Filling the gap between a distributional shift and stretch

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  • Kirkegaard, René

Abstract

I consider first-price auctions (FPA) and second-price auctions (SPA) with two asymmetric bidders. The FPA is known to be more profitable than the SPA if the strong bidder's distribution function is convex and the weak bidder's distribution is obtained by truncating or horizontally shifting the former. In this paper, I employ a new mechanism design result to show that the FPA remains optimal if the weak bidder's distribution falls between the two benchmarks in a natural way. The same conclusion holds if the strong bidder's distribution is concave, but with a vertical shift replacing the horizontal shift. A result with a similar flavor holds if the strong bidder's distribution is neither convex nor concave. The dispersive order and the star order prove useful in comparing the weak bidder's distribution to the benchmarks. A key step establishes a relationship between these orders and reverse hazard rate dominance.

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  • Kirkegaard, René, 2014. "Ranking asymmetric auctions: Filling the gap between a distributional shift and stretch," Games and Economic Behavior, Elsevier, vol. 85(C), pages 60-69.
    • Handle: RePEc:eee:gamebe:v:85:y:2014:i:c:p:60-69
    DOI: 10.1016/j.geb.2014.01.016
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    Cited by:

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    2. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Schweizer, Nikolaus & Szech, Nora, 2017. "Revenues and welfare in auctions with information release," Journal of Economic Theory, Elsevier, vol. 170(C), pages 86-111.
    4. Muhammed Ceesay & Nicola Doni & Domenico Menicucci, 2024. "Asymmetric Auctions with Discretely Distributed Valuations," Working Papers - Economics wp2024_20.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    5. Rosa, Benjamin V., 2020. "Affirmative action subcontracting regulations in dynamic procurement auctions," International Journal of Industrial Organization, Elsevier, vol. 72(C).
    6. Abraham, Ittai & Athey, Susan & Babaioff, Moshe & Grubb, Michael D., 2020. "Peaches, lemons, and cookies: Designing auction markets with dispersed information," Games and Economic Behavior, Elsevier, vol. 124(C), pages 454-477.

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    More about this item

    Keywords

    Asymmetric auctions; Dispersive order; Revenue ranking; Star order;
    All these keywords.

    JEL classification:

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

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