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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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Bibliographic 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
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
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.
  3. 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.
  4. 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.
  5. Lebrun, Bernard, 1996. "Existence of an Equilibrium in First Price Auctions," Economic Theory, Springer, vol. 7(3), pages 421-43, April.
  6. Olivier Armantier and 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.
  7. Philip J Reny, 2005. "On the Existence of Monotone Pure Strategy Equilibria in Bayesian Games," NajEcon Working Paper Reviews 784828000000000413, www.najecon.org.
  8. David Mcadams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," Review of Economic Studies, Wiley Blackwell, vol. 73(4), pages 1039-1056, October.
  9. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  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.
  11. 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.
  12. Jérémie Gallien & Shobhit Gupta, 2007. "Temporary and Permanent Buyout Prices in Online Auctions," Management Science, INFORMS, vol. 53(5), pages 814-833, May.
  13. Philip J. Reny & Shmuel Zamir, 2002. "On the Existence of Pure Strategy Monotone Equilibria in Asymmetric First-Price Auctions," Discussion Paper Series dp292, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  14. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
  15. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  16. 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.
  17. 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.
  18. Bernard Lebrun, 1996. "Existence of an equilibrium in first price auctions (*)," Economic Theory, Springer, vol. 7(3), pages 421-443.
  19. Armantier, O. & Florens, J.-P. & Richard, J.-F., 1997. "Equilibre approximatif et regle intuitive: une application aux appels d'offres dans l'industrie spatiale," Papers 97.487, Toulouse - GREMAQ.
  20. 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.
  21. Robert C. Marshall & Matthew E. Raiff & Jean-Francois Richard & Steven P. Schulenberg, 2006. "The Impact of Delivery Synergies on Bidding in the Georgia School Milk Market," The B.E. Journal of Economic Analysis & Policy, Berkeley Electronic Press, vol. 0(1), pages 5.
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