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Approximation of Nash equilibria in Bayesian games

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Author Info
Olivier Armantier (Federal Reserve Bank of New York; University of Montreal; CIRANO and CIREQ, Montreal, Canada)
Jean-Pierre Florens (Toulouse School of Economics, France)
Jean-Francois Richard (Department of Economics, University of Pittsburgh, Pennsylvania, USA)
Abstract

We define a new concept of constrained strategic equilibrium (CSE) for Bayesian games. We show that a sequence of CSEs approximates an equilibrium under standard conditions. We also provide an algorithm to implement the CSE approximation method numerically in a broad class of Bayesian games, including games without analytically tractable solutions. Finally, we illustrate the flexibility of the CSE approximation with a series of auction examples, including a complex multi-unit auction. Copyright © 2008 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.1040
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File URL: http://qed.econ.queensu.ca:80/jae/2008-v23.7/
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Publisher Info
Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 23 (2008)
Issue (Month): 7 ()
Pages: 965-981
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Handle: RePEc:jae:japmet:v:23:y:2008:i:7:p:965-981

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  1. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
  2. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, 07. [Downloadable!] (restricted)
  3. Bernard Lebrun, 1996. "Existence of an equilibrium in first price auctions (*)," Economic Theory, Springer, vol. 7(3), pages 421-443.
  4. Philip J. Reny & Shmuel Zamir, 2004. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Econometrica, Econometric Society, vol. 72(4), pages 1105-1125, 07. [Downloadable!] (restricted)
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  5. David Mcadams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," Review of Economic Studies, Blackwell Publishing, vol. 73(4), pages 1039-1056, October. [Downloadable!] (restricted)
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  6. 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. [Downloadable!] (restricted)
  7. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Blackwell Publishing, vol. 67(3), pages 439-54, July.
  8. Engelbrecht-Wiggans, Richard & Kahn, Charles M., 1998. "Multi-Unit Pay-Your-Bid Auctions with Variable Awards," Games and Economic Behavior, Elsevier, vol. 23(1), pages 25-42, April. [Downloadable!] (restricted)
  9. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321. [Downloadable!] (restricted)
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  10. Matias Eklöf, 2005. "Assessing Social Costs Of Inefficient Procurement Design," Journal of the European Economic Association, MIT Press, vol. 3(4), pages 826-850, 06. [Downloadable!] (restricted)
  11. Lebrun, Bernard, 1996. "Existence of an Equilibrium in First Price Auctions," Economic Theory, Springer, vol. 7(3), pages 421-43, April.
  12. MacKie-Mason, Jeffrey K. & Wellman, Michael P., 2006. "Automated Markets and Trading Agents," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 28, pages 1381-1431 Elsevier. [Downloadable!] (restricted)
  13. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May. [Downloadable!] (restricted)
  14. 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.
  15. Van Zandt, Timothy & Vives, Xavier, 2007. "Monotone equilibria in Bayesian games of strategic complementarities," Journal of Economic Theory, Elsevier, vol. 134(1), pages 339-360, May. [Downloadable!] (restricted)
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  16. Erwann SbaÏ & 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. [Downloadable!]
  17. Robert Marshall & Matthew Raiff & Jean-Francois Richard & Steven Schulenberg, 2006. "The Impact of Delivery Synergies on Bidding in the Georgia School Milk Market," Topics in Economic Analysis & Policy, Berkeley Electronic Press, vol. 6(1), pages 1327-1327. [Downloadable!] (restricted)
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