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Approximation of Nash equilibria in Bayesian games

Author

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  • 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.

Suggested Citation

  • 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.
    • Handle: RePEc:jae:japmet:v:23:y:2008:i:7:p:965-981
    DOI: 10.1002/jae.1040
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    2. Shiying Chen & Zhenhuan Dong & Chunming Cao & Changjun Zheng, 2022. "Strategy and design of multi‐unit auction in grouped asymmetric setting," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(8), pages 3435-3453, December.
    3. Bichler, Martin & Kohring, Nils & Oberlechner, Matthias & Pieroth, Fabian R., 2023. "Learning equilibrium in bilateral bargaining games," European Journal of Operational Research, Elsevier, vol. 311(2), pages 660-678.
    4. Ollikka, Kimmo & Tukiainen, Janne, 2013. "Central bank liquidity auction mechanism design and the interbank market," Research Discussion Papers 21/2013, Bank of Finland.
    5. 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.
    6. repec:zbw:bofrdp:2013_021 is not listed on IDEAS
    7. Ollikka, Kimmo & Tukiainen, Janne, 2013. "Central bank liquidity auction mechanism design and the interbank market," Bank of Finland Research Discussion Papers 21/2013, Bank of Finland.
    8. Martin Bichler & Nils Kohring & Stefan Heidekrüger, 2023. "Learning Equilibria in Asymmetric Auction Games," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 523-542, May.
    9. Pycia, Marek & Woodward, Kyle, 2021. "Auctions of Homogeneous Goods: A Case for Pay-as-Bid," CEPR Discussion Papers 15656, C.E.P.R. Discussion Papers.
    10. Wittwer, Milena, 2020. "Interconnected pay-as-bid auctions," Games and Economic Behavior, Elsevier, vol. 121(C), pages 506-530.

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