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A First Price Auction with an Arbitrary Number of Asymmetric Bidders

Author

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  • Doni Nicola

    (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze, Via delle Pandette 32, I-50127Firenze (FI), Italy)

  • Menicucci Domenico

    (Dipartimento di Scienze per l’Economia e l’Impresa, Università degli Studi di Firenze, Via delle Pandette 32, I-50127Firenze (FI), Italy)

Abstract

We examine an auction setting with private values and n≥2$n\geq 2$ bidders, which differ in the probability to have a low (high) value. We prove that for the first price auction, the equilibrium strategies can be written in closed form and there are gaps in the equilibrium bid distribution of each bidder except the strongest two. Our equilibrium characterization allows to prove that in this setting the seller prefers the second price auction to the first price auction for each n≥2$n\geq 2$.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:bejtec:v:19:y:2019:i:2:p:7:n:12
    DOI: 10.1515/bejte-2018-0105
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    References listed on IDEAS

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    1. Cheng, Harrison, 2006. "Ranking sealed high-bid and open asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 471-498, August.
    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. 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. Todd Kaplan & Shmuel Zamir, 2012. "Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 269-302, June.
    5. 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.
    6. Riley, John G, 1989. "Expected Revenue from Open and Sealed Bid Auctions," Journal of Economic Perspectives, American Economic Association, vol. 3(3), pages 41-50, Summer.
    7. René Kirkegaard, 2012. "A Mechanism Design Approach to Ranking Asymmetric Auctions," Econometrica, Econometric Society, vol. 80(5), pages 2349-2364, September.
    8. Rentschler, Lucas & Turocy, Theodore L., 2016. "Two-bidder all-pay auctions with interdependent valuations, including the highly competitive case," Journal of Economic Theory, Elsevier, vol. 163(C), pages 435-466.
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    More about this item

    Keywords

    first price auction; asymmetric bidders;

    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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