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SHARP TEST FOR EQUILIBRIUM UNIQUENESS IN DISCRETE GAMES WITH PRIVATE INFORMATION AND COMMON KNOWLEDGE UNOBSERVED HETEROGENEITY

Published online by Cambridge University Press:  16 March 2023

Mathieu Marcoux Open the ORCID record for Mathieu Marcoux [Opens in a new window]
Mathieu Marcoux*
Affiliation:
Université de Montréal
*
Address correspondence to Mathieu Marcoux, Département de sciences économiques, Université de Montréal, Centre-Ville, Montréal, QC H3C 3J7, Canada; e-mail: mathieu.marcoux@umontreal.ca.
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Abstract

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This paper proposes a testof the single equilibrium in the data assumption commonly maintained when estimating static discrete games of incomplete information. By allowing for discrete common knowledge payoff-relevant unobserved heterogeneity, the test generalizes existing methods attributing all correlation betweenplayers’ decisions to multiple equilibria. It does not require the estimation of payoffs and is therefore useful in empirical applications leveraging multiple equilibria to identify the model’s primitives. The procedure boils down to testing the emptiness of the set of data generating processes that can rationalize the sample through a single equilibrium and a finite mixture over unobserved heterogeneity. Under verifiable conditions, this testable implication is generically sufficient for degenerate equilibrium selection. The main identifying assumption is the existence of an observable variable that plays the role of a proxy for the unobservable heterogeneity. Examples of such proxies are provided based on empirical applications from the existing literature.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 6 , December 2024 , pp. 1253 - 1310
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Footnotes

I thank Victor Aguirregabiria, Andrés Aradillas-López, Vincent Boucher, Martin Burda, Karim Chalak, Christian Gouriéroux, Paul Grieco, Marc Henry, Yingyao Hu, Yao Luo, Ismael Mourifié, Joris Pinkse, Eduardo Souza Rodrigues, Thomas Russell, Yuanyuan Wan, and Ruli Xiao for comments and insightful discussions. I benefited from the comments of several seminar participants at Penn State, University of Toronto, Canadian Econometrics Study Group 2021, and IO Canada Conference 2021. Finally, I thank Christopher Ferrall for useful coding advice. All errors are mine. Financial support from the Social Sciences and Humanities Research Council (SSHRC) and Ontario Graduate Scholarship (OGS) is gratefully acknowledged.

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