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Testing The Quantal Response Hypothesis

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  • Emerson Melo
  • Kirill Pogorelskiy
  • Matthew Shum

Abstract

We develop a nonparametric test for consistency of player behavior with the quantal response equilibrium (QRE). The test exploits a characterization of the equilibrium choice probabilities in any structural QRE as the gradient of a convex function; thereby, QRE‐consistent choices satisfy the cyclic monotonicity inequalities. Our testing procedure utilizes recent econometric results for moment inequality models. We assess our test using lab experimental data from a series of generalized matching pennies games. We reject the QRE hypothesis in the pooled data but cannot reject individual‐level quantal response behavior for over half of the subjects.

Suggested Citation

  • Emerson Melo & Kirill Pogorelskiy & Matthew Shum, 2019. "Testing The Quantal Response Hypothesis," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(1), pages 53-74, February.
    • Handle: RePEc:wly:iecrev:v:60:y:2019:i:1:p:53-74
    DOI: 10.1111/iere.12344
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    Citations

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    Cited by:

    1. Sørensen, Jesper R.-V. & Fosgerau, Mogens, 2022. "How McFadden met Rockafellar and learned to do more with less," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    2. Emerson Melo, 2022. "On the uniqueness of quantal response equilibria and its application to network games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 681-725, October.
    3. Khai Xiang Chiong & Matthew Shum, 2019. "Random Projection Estimation of Discrete-Choice Models with Large Choice Sets," Management Science, INFORMS, vol. 65(1), pages 256-271, January.
    4. Alan Kirman & François Laisney & Paul Pezanis-Christou, 2023. "Relaxing the symmetry assumption in participation games: a specification test for cluster-heterogeneity," Experimental Economics, Springer;Economic Science Association, vol. 26(4), pages 850-878, September.
    5. Dagsvik, John K., 2020. "Equilibria in Logit Models of Social Interaction and Quantal Response Equilibrium," HERO Online Working Paper Series 2020:5, University of Oslo, Health Economics Research Programme, revised 09 Mar 2023.
    6. Fosgerau, Mogens & Melo, Emerson & Shum, Matthew & Sørensen, Jesper R.-V., 2021. "Some remarks on CCP-based estimators of dynamic models," Economics Letters, Elsevier, vol. 204(C).
    7. Roy Allen & John Rehbeck, 2021. "A Generalization of Quantal Response Equilibrium via Perturbed Utility," Games, MDPI, vol. 12(1), pages 1-16, March.

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