IDEAS home Printed from https://ideas.repec.org/p/bca/bocawp/24-24.html
   My bibliography  Save this paper

Non-Parametric Identification and Testing of Quantal Response Equilibrium

Author

Listed:
  • Johannes Hoelzemann
  • Ryan Webb
  • Erhao Xie

Abstract

We study the falsifiability and identification of Quantal Response Equilibrium (QRE) when each player’s utility and error distribution are relaxed to be unknown non-parametric functions. Using variations of players’ choices across a series of games, we first show that both the utility function and the distribution of errors are non-parametrically over-identified. This result further suggests a straightforward testing procedure for QRE that achieves the desired type-1 error and maintains a small type-2 error. To apply this methodology, we conduct an experimental study of the matching pennies game. Our non-parametric estimates strongly reject the conventional logit choice probability. Moreover, when the utility and the error distribution are sufficiently flexible and heterogeneous, the quantal response hypothesis cannot be rejected for 70% of participants. However, strong assumptions such as risk neutrality, logistically distributed errors and homogeneity lead to substantially higher rejection rates.

Suggested Citation

  • Johannes Hoelzemann & Ryan Webb & Erhao Xie, 2024. "Non-Parametric Identification and Testing of Quantal Response Equilibrium," Staff Working Papers 24-24, Bank of Canada.
    • Handle: RePEc:bca:bocawp:24-24
    as

    Download full text from publisher

    File URL: https://www.bankofcanada.ca/2024/06/staff-working-paper-2024-24/
    File Function: Abstract
    Download Restriction: no
    File URL: https://www.bankofcanada.ca/wp-content/uploads/2024/06/swp2024-24.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. James C. Cox & Glenn W. Harrison, 2008. "Risk aversion in experiments: An introduction," Research in Experimental Economics, in: Risk Aversion in Experiments, pages 1-7, Emerald Group Publishing Limited.
    2. Roy Allen & John Rehbeck, 2021. "A Generalization of Quantal Response Equilibrium via Perturbed Utility," Games, MDPI, vol. 12(1), pages 1-16, March.
    3. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    4. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    5. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fosgerau, Mogens & Bierlaire, Michel, 2007. "A practical test for the choice of mixing distribution in discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 784-794, August.
    2. Mittelhammer, Ron C. & Judge, George, 2011. "A family of empirical likelihood functions and estimators for the binary response model," Journal of Econometrics, Elsevier, vol. 164(2), pages 207-217, October.
    3. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1025-1106, Elsevier.
    4. Ron Mittelhammer & George Judge, 2009. "A Minimum Power Divergence Class of CDFs and Estimators for the Binary Choice Model," International Econometric Review (IER), Econometric Research Association, vol. 1(1), pages 33-49, April.
    5. Ye, Xin & Garikapati, Venu M. & You, Daehyun & Pendyala, Ram M., 2017. "A practical method to test the validity of the standard Gumbel distribution in logit-based multinomial choice models of travel behavior," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 173-192.
    6. Breitmoser, Yves, 2019. "Knowing me, imagining you: Projection and overbidding in auctions," Games and Economic Behavior, Elsevier, vol. 113(C), pages 423-447.
    7. Jose Apesteguia & Miguel A. Ballester, 2014. "Discrete choice estimation of risk aversion," Economics Working Papers 1443, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Emerson Melo, 2021. "Learning in Random Utility Models Via Online Decision Problems," Papers 2112.10993, arXiv.org, revised Aug 2022.
    9. Xie, Erhao, 2021. "Empirical properties and identification of adaptive learning models in behavioral game theory," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 798-821.
    10. Bergtold, Jason S. & Ramsey, Steven M., 2015. "Neural Network Estimators of Binary Choice Processes: Estimation, Marginal Effects and WTP," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205649, Agricultural and Applied Economics Association.
    11. Fan Wu & Yi Xin, 2024. "Estimating Nonseparable Selection Models: A Functional Contraction Approach," Papers 2411.01799, arXiv.org, revised Feb 2025.
    12. Bart Capéau & Liebrecht De Sadeleer & Sebastiaan Maes & André Decoster, 2020. "Nonparametric welfare analysis for discrete choice: levels and differences of individual and social welfare," Working Papers of Department of Economics, Leuven 674666, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    13. Roy Allen & John Rehbeck, 2021. "A Generalization of Quantal Response Equilibrium via Perturbed Utility," Games, MDPI, vol. 12(1), pages 1-16, March.
    14. Aradillas-Lopez, Andres, 2012. "Pairwise-difference estimation of incomplete information games," Journal of Econometrics, Elsevier, vol. 168(1), pages 120-140.
    15. Mogens Fosgerau, 2024. "Nonparametric approaches to describing heterogeneity," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 11, pages 308-318, Edward Elgar Publishing.
    16. S. Cerreia-Vioglio & F. Maccheroni & M. Marinacci & A. Rustichini, 2017. "Multinomial logit processes and preference discovery: inside and outside the black box," Working Papers 615, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    17. Jehiel, Philippe & Singh, Juni, 2021. "Multi-state choices with aggregate feedback on unfamiliar alternatives," Games and Economic Behavior, Elsevier, vol. 130(C), pages 1-24.
    18. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2020. "Multinomial logit processes and preference discovery: outside and inside the black box," Working Papers 663, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    19. Steven M. Ramsey & Jason S. Bergtold, 2021. "Examining Inferences from Neural Network Estimators of Binary Choice Processes: Marginal Effects, and Willingness-to-Pay," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1137-1165, December.
    20. Breitmoser, Yves, 2010. "Hierarchical Reasoning versus Iterated Reasoning in p-Beauty Contest Guessing Games," MPRA Paper 19893, University Library of Munich, Germany.

    More about this item

    Keywords

    Econometric and statistical methods; Economic models;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bca:bocawp:24-24. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bocgvca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.