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Estimating Simultaneous Games with Incomplete Information under Median Restrictions

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  • Xun Tang

    () (Department of Economics, University of Pennsylvania)

Abstract

I estimate a simultaneous discrete game with incomplete information where players’ private information are only required to be median independent of observed states and can be correlated with observable states. This median restriction is weaker than other assumptions on players’ private information in the literature (e.g. perfect knowledge of its distribution or its independence of the observable states). I show index coefficients in players’ utility functions are point-identified under an exclusion restriction and fairly weak conditions on the support of states. This identification strategy is fundamentally different from that in a single-agent binary response models with median restrictions, and does not involve any parametric assumption on equilibrium selection in the presence of multiple Bayesian Nash equilibria. I then propose a two-step extreme estimator for the linear coefficients, and prove its consistency.

Suggested Citation

  • Xun Tang, 2009. "Estimating Simultaneous Games with Incomplete Information under Median Restrictions," PIER Working Paper Archive 09-023, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:09-023
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    File URL: http://economics.sas.upenn.edu/system/files/working-papers/09-023.pdf
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    References listed on IDEAS

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    1. Bajari, Patrick & Hong, Han & Krainer, John & Nekipelov, Denis, 2010. "Estimating Static Models of Strategic Interactions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 469-482.
    2. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, 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. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
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    Cited by:

    1. Antonio Merlo & Xun Tang, 2009. "Identification of Stochastic Sequential Bargaining Models," PIER Working Paper Archive 09-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

    More about this item

    Keywords

    Games with incomplete information; semiparametric identification; median restrictions; consistent estimation;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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