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Non-Parametric Identification and Testing of Quantal Response Equilibrium

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  • 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
    DOI: 10.34989/swp-2024-24
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    References listed on IDEAS

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    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. 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.
    4. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, January.
    5. 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.
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    Keywords

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    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

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