On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm
AbstractWe describe and compare numerical methods used to approximate equilibrium bid functions in models of auctions as games of incomplete information. In such games, private values are modelled as draws from bidder-specific type distributions and pay-your-bid rules are used to determine transactions prices. We provide a formal comparison of the performance of these numerical methods (based on speed and accuracy) and suggest ways in which they can be improved and extended as well as applied to new settings.
Download InfoIf 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.
Bibliographic InfoPaper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 291.
Length: 111 pages
Date of creation: 2012
Date of revision:
first-price auctions; asymmetric auctions; private-values model; numerical solutions.;
Find related papers by JEL classification:
- C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
- D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
- L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
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.:
- J. Riley & E. Maskin, 1981.
"Optimal Auctions with Risk Averse Buyers,"
311, Massachusetts Institute of Technology (MIT), Department of Economics.
- Matthews, Steven A., 1983.
"Selling to risk averse buyers with unobservable tastes,"
Journal of Economic Theory,
Elsevier, vol. 30(2), pages 370-400, August.
- Steven A. Matthews, 1981. "Selling to Risk Averse Buyers with Unobservable Tastes," Discussion Papers 480S, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
- Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
- Che‐Lin Su & Kenneth L. Judd, 2012.
"Constrained Optimization Approaches to Estimation of Structural Models,"
Econometric Society, vol. 80(5), pages 2213-2230, 09.
- Che-Lin Su & Kenneth L. Judd, 2008. "Constrainted Optimization Approaches to Estimation of Structural Models," Discussion Papers 1460, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Lizzeri, Alessandro & Persico, Nicola, 2000. "Uniqueness and Existence of Equilibrium in Auctions with a Reserve Price," Games and Economic Behavior, Elsevier, vol. 30(1), pages 83-114, January.
- Hubbard, Timothy P. & Li, Tong & Paarsch, Harry J., 2011.
"Semiparametric Estimation in Models of First-Price, Sealed-Bid Auctions with Affiliation,"
CEI Working Paper Series
2010-10, Center for Economic Institutions, Institute of Economic Research, Hitotsubashi University.
- Hubbard, Timothy P. & Li, Tong & Paarsch, Harry J., 2012. "Semiparametric estimation in models of first-price, sealed-bid auctions with affiliation," Journal of Econometrics, Elsevier, vol. 168(1), pages 4-16.
- Eric Maskin & John Riley, 2003.
"Uniqueness of Equilibrium in Sealed High-Bid Auctions,"
Economics Working Papers
0031, Institute for Advanced Study, School of Social Science.
- Maskin, Eric & Riley, John, 2003. "Uniqueness of equilibrium in sealed high-bid auctions," Games and Economic Behavior, Elsevier, vol. 45(2), pages 395-409, November.
- Fibich, Gadi & Gavious, Arieh & Sela, Aner, 2004. "Revenue equivalence in asymmetric auctions," Journal of Economic Theory, Elsevier, vol. 115(2), pages 309-321, April.
- Viplav Saini, 2012. "Endogenous asymmetry in a dynamic procurement auction," RAND Journal of Economics, RAND Corporation, vol. 43(4), pages 726-760, December.
- Cheng, Harrison, 2006. "Ranking sealed high-bid and open asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 471-498, August.
- Paarsch, Harry J., 1997. "Deriving an estimate of the optimal reserve price: An application to British Columbian timber sales," Journal of Econometrics, Elsevier, vol. 78(2), pages 333-357, June.
- Erwann Sba� & Olivier Armantier, 2006.
"Estimation and comparison of treasury auction formats when bidders are asymmetric,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 21(6), pages 745-779.
- Olivier Armantier & Erwann Sbai, 2003. "Estimation and Comparison of Treasury Auction Formats when Bidders are Asymmetric," Department of Economics Working Papers 03-02, Stony Brook University, Department of Economics.
- Bali, Valentina & Jackson, Matthew, 2002. "Asymptotic Revenue Equivalence in Auctions," Journal of Economic Theory, Elsevier, vol. 106(1), pages 161-176, September.
- Cox, James C. & Smith, Vernon L. & Walker, James M., 1982. "Auction market theory of heterogeneous bidders," Economics Letters, Elsevier, vol. 9(4), pages 319-325.
- René Kirkegaard, 2012. "A Mechanism Design Approach to Ranking Asymmetric Auctions," Econometrica, Econometric Society, vol. 80(5), pages 2349-2364, 09.
- Elena Krasnokutskaya & Katja Seim, 2011. "Bid Preference Programs and Participation in Highway Procurement Auctions," American Economic Review, American Economic Association, vol. 101(6), pages 2653-86, October.
- Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
- Marion, Justin, 2007. "Are bid preferences benign? The effect of small business subsidies in highway procurement auctions," Journal of Public Economics, Elsevier, vol. 91(7-8), pages 1591-1624, August.
- 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.
- Olivier Armantier & Jean-Pierre Florens & Jean-Francois Richard, 2008. "Approximation of Nash equilibria in Bayesian games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(7), pages 965-981.
- Li, Huagang & Riley, John G., 2007. "Auction choice," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1269-1298, December.
- Athey, Susan, 2001.
"Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information,"
Econometric Society, vol. 69(4), pages 861-89, July.
- Athey, S., 1997. "Sigle Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Working papers 97-11, Massachusetts Institute of Technology (MIT), Department of Economics.
- Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
- Olivier ARMANTIER & Erwann SBAÏ, 2009. "Comparison of Alternative Payment Mechanisms for French Treasury Auctions," Annales d'Economie et de Statistique, ENSAE, issue 93-94, pages 135-160.
- Riley, John G & Samuelson, William F, 1981.
American Economic Review,
American Economic Association, vol. 71(3), pages 381-92, June.
- 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.
- 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.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Giovanni Bert).
If references are entirely missing, you can add them using this form.