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On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm

  • Timothy P. Hubbard
  • Harry J. Paarsch

We 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.

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File URL: http://www.carloalberto.org/assets/working-papers/no.291.pdf
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Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 291.

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Length: 111 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:cca:wpaper:291
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  1. J. Riley & E. Maskin, 1981. "Optimal Auctions with Risk Averse Buyers," Working papers 311, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. 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.
  3. 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.
  4. Li, Huagang & Riley, John G., 2007. "Auction choice," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1269-1298, December.
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  6. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, June.
  7. Viplav Saini, 2012. "Endogenous asymmetry in a dynamic procurement auction," RAND Journal of Economics, RAND Corporation, vol. 43(4), pages 726-760, December.
  8. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  9. 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.
  10. Bali, Valentina & Jackson, Matthew, 2002. "Asymptotic Revenue Equivalence in Auctions," Journal of Economic Theory, Elsevier, vol. 106(1), pages 161-176, September.
  11. 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.
  12. John G. Riley & William Samuelson, 1979. "Optimal Auctions," UCLA Economics Working Papers 152, UCLA Department of Economics.
  13. 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.
  14. 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.
  15. 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.
  16. René Kirkegaard, 2012. "A Mechanism Design Approach to Ranking Asymmetric Auctions," Econometrica, Econometric Society, vol. 80(5), pages 2349-2364, 09.
  17. Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
  18. 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.
  19. Fibich, Gadi & Gavious, Arieh & Sela, Aner, 2004. "Revenue equivalence in asymmetric auctions," Journal of Economic Theory, Elsevier, vol. 115(2), pages 309-321, April.
  20. 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.
  21. 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.
  22. Cheng, Harrison, 2006. "Ranking sealed high-bid and open asymmetric auctions," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 471-498, August.
  23. 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.
  24. 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.
  25. 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.
  26. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-89, July.
  27. Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
  28. 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.
  29. 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.
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