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Revenue Comparison in Asymmetric Auctions with Discrete Valuations

Author

Listed:
  • Doni Nicola

    (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze, Firenze, Italy)

  • Menicucci Domenico

    (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze, Firenze, Italy)

Abstract

We consider an asymmetric auction setting with two bidders such that the valuation of each bidder has a binary support. First, we characterize the unique equilibrium outcome in the first price auction for any values of parameters. Then we compare the first price auction with the second price auction in terms of expected revenue. Under the assumption that the probabilities of low values are the same for the two bidders, we obtain two main results: (i) the second price auction yields a higher revenue unless the distribution of a bidder’s valuation first-order stochastically dominates the distribution of the other bidder’s valuation “in a strong sense” and (ii) introducing reserve prices implies that the first price auction is never superior to the second price auction. In addition, in some cases, the revenue in the first price auction decreases when all the valuations increase.

Suggested Citation

  • Doni Nicola & Menicucci Domenico, 2013. "Revenue Comparison in Asymmetric Auctions with Discrete Valuations," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 429-461, September.
    • Handle: RePEc:bpj:bejtec:v:13:y:2013:i:1:p:33:n:9
    DOI: 10.1515/bejte-2012-0014
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    References listed on IDEAS

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    1. Bernard Lebrun, 2002. "Continuity of the first price auction Nash equilibrium correspondence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(3), pages 435-453.
    2. Rene Kirkegaard, 2011. "Ranking Asymmetric Auctions using the Dispersive Order," Working Papers 1101, University of Guelph, Department of Economics and Finance.
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    6. Nicola Doni & Domenico Menicucci, 2014. "Information Revelation in Procurement Auctions with Two‐Sided Asymmetric Information," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(4), pages 952-968, December.
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    9. Doni Nicola & Menicucci Domenico, 2013. "Revenue Comparison in Asymmetric Auctions with Discrete Valuations," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 429-461, September.
    10. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-86, July.
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    Citations

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    Cited by:

    1. Yew-Kwang Ng, 2016. "Are Unrealistic Assumptions/Simplifications Acceptable? Some Methodological Issues in Economics," Pacific Economic Review, Wiley Blackwell, vol. 21(2), pages 180-201, May.
    2. Doni Nicola & Menicucci Domenico, 2013. "Revenue Comparison in Asymmetric Auctions with Discrete Valuations," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 429-461, September.
    3. Doni Nicola & Menicucci Domenico, 2019. "A First Price Auction with an Arbitrary Number of Asymmetric Bidders," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 19(2), pages 1-7, June.
    4. Cohensius Gal & Segev Ella, 2018. "Sequential Bidding in Asymmetric First Price Auctions," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-21, January.
    5. Nicola Doni & Domenico Menicucci, 2014. "Information Revelation in Procurement Auctions with Two‐Sided Asymmetric Information," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(4), pages 952-968, December.
    6. Kyungmin Kim & Youngwoo Koh, 2019. "Efficiency and Revenue in Asymmetric Auctions," Korean Economic Review, Korean Economic Association, vol. 35, pages 371-391.
    7. Kirkegaard, René, 2021. "Ranking reversals in asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    8. Andrzej Baranski & Sumit Goel, 2024. "Contest design with a finite type-space: A unifying approach," Papers 2410.04970, arXiv.org, revised Oct 2024.
    9. 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.

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    More about this item

    Keywords

    asymmetric auctions; first price auctions; second price auctions;
    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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