Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions
In models of first-price auctions, when bidders are ex ante heterogeneous, deriving explicit equilibrium bid functions is typically impossible, so numerical methods are often employed to find approximate solutions. Recent theoretical research concerning asymmetric auctions has determined some properties these bid functions must satisfy when certain conditions are met. Plotting the relative expected pay-offs of bidders is a quick, informative way to decide whether the approximate solutions are consistent with theory. We approximate the (inverse-)bid functions by polynomials and employ theoretical results in two ways: to help solve for the polynomial coefficients and to evaluate qualitatively the appropriateness of a given approximation. We simulate auctions from the approximated solutions and find that, for the examples considered, low-degree polynomial approximations perform poorly and can lead to incorrect policy recommendations concerning auction design, suggesting researchers need to take care to obtain quality solutions. Copyright Springer Science+Business Media New York 2013
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 42 (2013)
Issue (Month): 2 (August)
|Contact details of provider:|| Web page: http://www.springerlink.com/link.asp?id=100248|
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Fibich, Gadi & Gavious, Arieh & Sela, Aner, 2004. "Revenue equivalence in asymmetric auctions," Journal of Economic Theory, Elsevier, vol. 115(2), pages 309-321, April.
- Bernard Lebrun, 2004.
"Uniqueness of the Equilibrium in First-Price Auctions,"
1, York University, Department of Economics, revised May 2004.
- Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
- Bernard Lebrun, 2004. "Uniqueness of the Equilibrium in First-Price Auctions," Working Papers 2004_2, York University, Department of Economics.
- Brendstrup, Bjarne & Paarsch, Harry J., 2006. "Identification and estimation in sequential, asymmetric, English auctions," Journal of Econometrics, Elsevier, vol. 134(1), pages 69-94, September.
- Wayne-Roy Gayle & Jean Richard, 2008. "Numerical Solutions of Asymmetric, First-Price, Independent Private Values Auctions," Computational Economics, Society for Computational Economics, vol. 32(3), pages 245-278, October.
- Marshall Robert C. & Meurer Michael J. & Richard Jean-Francois & Stromquist Walter, 1994. "Numerical Analysis of Asymmetric First Price Auctions," Games and Economic Behavior, Elsevier, vol. 7(2), pages 193-220, September.
- Li, Huagang & Riley, John G., 2007. "Auction choice," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1269-1298, December.
- 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.
- Estelle Cantillon, 2008. "The effect of bidders' asymmetries on expected revenue in auctions," ULB Institutional Repository 2013/9001, ULB -- Universite Libre de Bruxelles.
- Estelle Cantillon, 2000. "The Effect of Bidders' Asymmetries on Expected Revenue in Auctions," Cowles Foundation Discussion Papers 1279, Cowles Foundation for Research in Economics, Yale University.
- Fibich, Gadi & Gavious, Arieh & Sela, Aner, 2002. "Low and high types in asymmetric first-price auctions," Economics Letters, Elsevier, vol. 75(2), pages 283-287, April.
- Lebrun, Bernard, 1999.
"First Price Auctions in the Asymmetric N Bidder Case,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-42, February.
- Lebrun, Bernard, 1997. "First Price Auctions in the Asymmetric N Bidder Case," Cahiers de recherche 9715, Université Laval - Département d'économique.
- Hubbard, Timothy P. & Paarsch, Harry J., 2009. "Investigating bid preferences at low-price, sealed-bid auctions with endogenous participation," International Journal of Industrial Organization, Elsevier, vol. 27(1), pages 1-14, January.
- William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
- Todd Kaplan & Shmuel Zamir, 2012. "Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case," Economic Theory, Springer, vol. 50(2), pages 269-302, June.
- Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
- 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.
- Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, March.
- Guerre, E. & Perrigne, I. & Vuong, Q., 1995. "Nonparametric Estimation of First-Price Auctions," Papers 9504, Southern California - Department of Economics.
- Arieh Gavious & Yizhaq Minchuk, 2014. "Ranking asymmetric auctions," International Journal of Game Theory, Springer, vol. 43(2), pages 369-393, May.
- Fibich, Gadi & Gavish, Nir, 2011. "Numerical simulations of asymmetric first-price auctions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 479-495.
- Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
- Cheng, Harrison, 2006. "Ranking sealed high-bid and open asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 471-498, August.
- Viplav Saini, 2012. "Endogenous asymmetry in a dynamic procurement auction," RAND Journal of Economics, RAND Corporation, vol. 43(4), pages 726-760, December.
When requesting a correction, please mention this item's handle: RePEc:kap:compec:v:42:y:2013:i:2:p:241-266. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Rebekah McClure)
If references are entirely missing, you can add them using this form.