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Sharp identification regions in games

Author

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  • Arie Beresteanu

    () (Institute for Fiscal Studies and University of Pittsburgh)

  • Ilya Molchanov

    () (Institute for Fiscal Studies and University of Bern, Institute of Mathematical Statistics and Actuarial Science)

  • Francesca Molinari

    () (Institute for Fiscal Studies and Cornell University)

Abstract

We study identification in static, simultaneous move finite games of complete information, where the presence of multiple Nash equilibria may lead to partial identification of the model parameters. The identification regions for these parameters proposed in the related literature are known not to be sharp. Using the theory of random sets, we show that the sharp identification region can be obtained as the set of minimizers of the distance from the conditional distribution of game's outcomes given covariates, to the conditional Aumann expectation given covariates of a properly defined random set. This is the random set of probability distributions over action profiles given profit shifters implied by mixed strategy Nash equilibria. The sharp identification region can be approximated arbitrarily accurately through a finite number of moment inequalities based on the support function of the conditional Aumann expectation. When only pure strategy Nash equilibria are played, the sharp identification region is exactly determined by a finite number of moment inequalities. We discuss how our results can be extended to other solution concepts, such as for example correlated equilibrium or rationality and rationalizability. We show that calculating the sharp identification region using our characterization is computationally feasible. We also provide a simple algorithm which finds the set of inequalities that need to be checked in order to insure sharpness. We use examples analyzed in the literature to illustrate the gains in identification afforded by our method.

Suggested Citation

  • Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2008. "Sharp identification regions in games," CeMMAP working papers CWP15/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:15/08
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    File URL: http://cemmap.ifs.org.uk/wps/cwp1508.pdf
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    References listed on IDEAS

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    1. repec:pit:wpaper:428 is not listed on IDEAS
    2. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    3. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    4. Steven N. Durlauf & Yannis M. Ioannides, 2010. "Social Interactions," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 451-478, September.
    5. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    6. Marc HENRY & Ismael MOURIFIÉ, 2013. "Nonparametric Sharp Bounds For Payoffs In 2 × 2 Games," Working Papers tecipa-500, University of Toronto, Department of Economics.
    7. Alberto Bisin & Andrea Moro & Giorgio Topa, 2011. "The empirical content of models with multiple equilibria in economies with social interactions," Staff Reports 504, Federal Reserve Bank of New York.
    8. Beresteanu, Arie & Molchanov, Ilya & Molinari, Francesca, 2012. "Partial identification using random set theory," Journal of Econometrics, Elsevier, vol. 166(1), pages 17-32.
    9. Liran Einav, 2010. "Not All Rivals Look Alike: Estimating An Equilibrium Model Of The Release Date Timing Game," Economic Inquiry, Western Economic Association International, vol. 48(2), pages 369-390, April.
    10. Paul L. E. Grieco, 2014. "Discrete games with flexible information structures: an application to local grocery markets," RAND Journal of Economics, RAND Corporation, vol. 45(2), pages 303-340, June.
    11. repec:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    12. Marc Henry & Ismael Mourifié, 2012. "Sharp Bounds in the Binary Roy Model," CIRJE F-Series CIRJE-F-835, CIRJE, Faculty of Economics, University of Tokyo.
    13. Giorgio Topa & Elizabeth Setren & Meta Brown, 2011. "Do Referrals Lead to Better Matches? Evidence from a Firm's Employee," 2011 Meeting Papers 711, Society for Economic Dynamics.
    14. Marc Henry & Romuald Méango & Maurice Queyranne, 2012. "Combinatorial Bootstrap Inference IN in Prtially Identified Incomplete Structural Models," CIRJE F-Series CIRJE-F-837, CIRJE, Faculty of Economics, University of Tokyo.
    15. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, vol. 80(6), pages 2805-2826, November.
    16. Jeremy T. Fox, 2008. "Estimating Matching Games with Transfers," NBER Working Papers 14382, National Bureau of Economic Research, Inc.
    17. Aradillas-Lopez, Andres, 2012. "Pairwise-difference estimation of incomplete information games," Journal of Econometrics, Elsevier, vol. 168(1), pages 120-140.
    18. J. Stoye, 2009. "Charles F. Manski, Identification for Prediction and Decision (Harvard University Press 2007)," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 857-862.

    More about this item

    Keywords

    Identification; Random Sets; Aumann Expectation; Support Function; Capacity Functional; Normal Form Games; Inequality Constraints.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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