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Revenue Comparison in Asymmetric Auctions with Discrete Valuations

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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Paper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Economics with number wp2011_08.rdf.

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Length: 32 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:frz:wpaper:wp2011_08.rdf
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  1. Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
  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. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-86, July.
  4. Arieh Gavious & Yizhaq Minchuk, 2014. "Ranking asymmetric auctions," International Journal of Game Theory, Springer, vol. 43(2), pages 369-393, May.
  5. 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.
  6. 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.
  7. Rene Kirkegaard, 2011. "Ranking Asymmetric Auctions using the Dispersive Order," Working Papers 1101, University of Guelph, Department of Economics and Finance.
  8. Li, Huagang & Riley, John G., 2007. "Auction choice," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1269-1298, December.
  9. Eric Maskin & John G. Riley, 1983. "Auctions with Asymmetric Beliefs," UCLA Economics Working Papers 254, UCLA Department of Economics.
  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.
  11. 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.
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