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Estimating Simultaneous Games with Incomplete Information under Median Restrictions

  • Xun Tang

    ()

    (Department of Economics, University of Pennsylvania)

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    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.

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    File URL: http://economics.sas.upenn.edu/system/files/working-papers/09-023.pdf
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    Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 09-023.

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    Length: 17 pages
    Date of creation: 30 Apr 2009
    Date of revision:
    Handle: RePEc:pen:papers:09-023
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    1. 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.
    2. Patrick Bajari & Han Hong & John Krainer & Denis Nekipelov, 2006. "Estimating Static Models of Strategic Interaction," NBER Working Papers 12013, National Bureau of Economic Research, Inc.
    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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