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Revenue Comparison in Asymmetric Auctions with Discrete Valuations

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Abstract

We consider an asymmetric auction setting with two bidders such that the valuation of each bidder has a binary support. We prove that in this context the second price auction yields a higher expected revenue than the first price auction for a broad set of parameter values, although the opposite result is common in the literature on asymmetric auctions. For instance, the second price auction is superior both when a bidder’s valuation is more uncertain that the valuation of the other bidder, and in case of a not too large distribution shift or rescaling. In addition, we show that in some cases the revenue in the first price auction decreases when all the valuations increase [in doing so, we correct a claim in Maskin and Riley (1985), and we derive the bidders’ preferences between the two auctions.

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  • Nicola Doni & Domenico Menicucci, 2011. "Revenue Comparison in Asymmetric Auctions with Discrete Valuations," Working Papers - Economics wp2011_08.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  • Handle: RePEc:frz:wpaper:wp2011_08.rdf
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    1. 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 1-33, September.
    2. Wayne-Roy Gayle & Jean Richard, 2008. "Numerical Solutions of Asymmetric, First-Price, Independent Private Values Auctions," Computational Economics, Springer;Society for Computational Economics, vol. 32(3), pages 245-278, October.
    3. Plum, M, 1992. "Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 393-418.
    4. 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.
    5. Arieh Gavious & Yizhaq Minchuk, 2014. "Ranking asymmetric auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 369-393, May.
    6. Maskin, Eric S & Riley, Joan G, 1985. "Auction Theory with Private Values," American Economic Review, American Economic Association, vol. 75(2), pages 150-155, May.
    7. Rene Kirkegaard, 2011. "Ranking Asymmetric Auctions using the Dispersive Order," Working Papers 1101, University of Guelph, Department of Economics and Finance.
    8. Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
    9. Cantillon, Estelle, 2008. "The effect of bidders' asymmetries on expected revenue in auctions," Games and Economic Behavior, Elsevier, vol. 62(1), pages 1-25, January.
    10. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    11. Eric Maskin & John G. Riley, 1983. "Auctions with Asymmetric Beliefs," UCLA Economics Working Papers 254, UCLA Department of Economics.
    12. Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
    13. 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.
    14. Eric Maskin & John Riley, 2000. "Equilibrium in Sealed High Bid Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 439-454.
    15. Cheng, Harrison, 2006. "Ranking sealed high-bid and open asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 471-498, August.
    16. Li, Huagang & Riley, John G., 2007. "Auction choice," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1269-1298, December.
    17. 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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    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 1-33, 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. 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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