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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://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

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Handle: RePEc:jae:japmet:v:23:y:2008:i:7:p:965-981

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References

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  2. Maskin, Eric & Riley, John, 2000. "Equilibrium in Sealed High Bid Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 439-54, July.
  3. 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.
  4. 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.
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  7. Lebrun, Bernard, 1996. "Existence of an Equilibrium in First Price Auctions," Economic Theory, Springer, vol. 7(3), pages 421-43, April.
  8. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
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  17. 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.
  18. 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.
  19. David McAdams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1039-1056.
  20. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
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Cited by:
  1. Timothy P. Hubbard & Harry J. Paarsch, 2012. "On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm," Carlo Alberto Notebooks 291, Collegio Carlo Alberto.
  2. Ollikka, Kimmo & Tukiainen , Janne, 2013. "Central bank liquidity auction mechanism design and the interbank market," Research Discussion Papers 21/2013, Bank of Finland.

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