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Revenue Comparison in Asymmetric Auctions with Discrete Valuations

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  • Doni Nicola

    ()

  • 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.

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Bibliographic Info

Article provided by De Gruyter in its journal The B.E. Journal of Theoretical Economics.

Volume (Year): 13 (2013)
Issue (Month): 1 (September)
Pages: 33

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Handle: RePEc:bpj:bejtec:v:13:y:2013:i:1:p:33:n:9

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  1. Maskin, Eric S & Riley, Joan G, 1985. "Auction Theory with Private Values," American Economic Review, American Economic Association, vol. 75(2), pages 150-55, May.
  2. Cheng, Harrison, 2006. "Ranking sealed high-bid and open asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 471-498, August.
  3. 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.
  4. Li, Huagang & Riley, John G., 2007. "Auction choice," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1269-1298, December.
  5. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-86, July.
  6. Eric Maskin & John G. Riley, 1983. "Auctions with Asymmetric Beliefs," UCLA Economics Working Papers 254, UCLA Department of Economics.
  7. Rene Kirkegaard, 2011. "Ranking Asymmetric Auctions using the Dispersive Order," Working Papers 1101, University of Guelph, Department of Economics and Finance.
  8. Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
  9. Plum, M, 1992. "Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information," International Journal of Game Theory, Springer, vol. 20(4), pages 393-418.
  10. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
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Cited by:
  1. Nicola Doni & Domenico Menicucci, 2011. "Information revelation in procurement auctions with two-sided asymmetric information," Working Papers - Economics wp2011_14.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.

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