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Inference for Games with Many Players

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  • Konrad Menzel

Abstract

We develop an asymptotic theory for static discrete-action games with a large number of players, and propose a novel inference approach based on stochastic expansions around the limit of the finite-player game. Our analysis focuses on anonymous games in which payoffs are a function of the agent's own action and the empirical distribution of her opponents' play. We establish a law of large numbers and central limit theorem which can be used to establish consistency of point or set estimators and asymptotic validity for inference on structural parameters as the number of players increases. The proposed methods as well as the limit theory are conditional on the realized equilibrium in the observed sample and therefore do not require any assumptions regarding selection among multiple equilibria.

Suggested Citation

  • Konrad Menzel, 2016. "Inference for Games with Many Players," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 83(1), pages 306-337.
    • Handle: RePEc:oup:restud:v:83:y:2016:i:1:p:306-337.
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    File URL: http://hdl.handle.net/10.1093/restud/rdv038
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    Citations

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    Cited by:

    1. Bryan S. Graham & Andrin Pelican, 2023. "Scenario Sampling for Large Supermodular Games," Papers 2307.11857, arXiv.org.
    2. Harold D. Chiang & Kengo Kato & Yuya Sasaki, 2023. "Inference for High-Dimensional Exchangeable Arrays," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(543), pages 1595-1605, July.
    3. Vincent Boucher & Yann Bramoullé, 2020. "Binary Outcomes and Linear Interactions," AMSE Working Papers 2038, Aix-Marseille School of Economics, France.
    4. Debopam Bhattacharya & Pascaline Dupas & Shin Kanaya, 2024. "Demand and Welfare Analysis in Discrete Choice Models with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(2), pages 748-784.
    5. Beare, Brendan K. & Seo, Juwon, 2020. "Randomization Tests Of Copula Symmetry," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1025-1063, December.
    6. Chen, Liang & Luo, Yao, 2023. "Empirical analysis of network effects in nonlinear pricing data," International Journal of Industrial Organization, Elsevier, vol. 91(C).
    7. Jacob Schwartz, 2018. "Schooling Choice, Labour Market Matching, and Wages," Papers 1803.09020, arXiv.org, revised Aug 2019.
    8. Daniel Lacker & Kavita Ramanan, 2019. "Rare Nash Equilibria and the Price of Anarchy in Large Static Games," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 400-422, May.
    9. Lin, Zhongjian & Hu, Yingyao, 2024. "Binary choice with misclassification and social interactions, with an application to peer effects in attitude," Journal of Econometrics, Elsevier, vol. 238(1).
    10. Pierre-André Chiappori & Bernard Salanié, 2016. "The Econometrics of Matching Models," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 832-861, September.
    11. Jorge Balat & Sukjin Han, 2018. "Multiple Treatments with Strategic Interaction," Papers 1805.08275, arXiv.org, revised Sep 2019.
    12. Bryan S. Graham & Andrin Pelican, 2023. "Scenario sampling for large supermodular games," CeMMAP working papers 15/23, Institute for Fiscal Studies.
    13. Geert Ridder & Shuyang Sheng, 2020. "Two-Step Estimation of a Strategic Network Formation Model with Clustering," Papers 2001.03838, arXiv.org, revised Nov 2022.
    14. Nathan Canen & Jacob Schwartz & Kyungchul Song, 2020. "Estimating local interactions among many agents who observe their neighbors," Quantitative Economics, Econometric Society, vol. 11(3), pages 917-956, July.
    15. Michael P. Leung, 2020. "Equilibrium computation in discrete network games," Quantitative Economics, Econometric Society, vol. 11(4), pages 1325-1347, November.
    16. Liang Chen & Yao Luo, 2023. "Empirical Analysis of Network Effects in Nonlinear Pricing Data," Working Papers tecipa-758, University of Toronto, Department of Economics.

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