IDEAS home Printed from https://ideas.repec.org/p/tex/wpaper/130911.html
   My bibliography  Save this paper

Semiparametric Analysis of Binary Games of Incomplete Information

Author

Listed:
  • Nianqing Liu

    (Shanghai University of Finance and Economics)

  • Haiqing Xu

    (Department of Economics, Texas University)

Abstract

This paper studies the identification and estimation in an I-player binary game of incomplete information. Our approach allows players' type to be correlated across players. By focusing on the monotone pure strategy Bayesian Nash Equilibrium (BNE), we show that the equilibrium strategies can be represented as a single-agent binary response model. Under weak restrictions, we show that the distribution of incomplete information can be nonparametrically identified. Further, we establish the identification of payoff functions in a linear-index setup. Following Klein and Spady (1993), we propose a three-stage estimation procedure and show that our estimator is square-root-n consistent, asymptotically normally distributed.

Suggested Citation

  • Nianqing Liu & Haiqing Xu, "undated". "Semiparametric Analysis of Binary Games of Incomplete Information," Department of Economics Working Papers 130911, The University of Texas at Austin, Department of Economics, revised Nov 2012.
    • Handle: RePEc:tex:wpaper:130911
    as

    Download full text from publisher

    File URL: https://webspace.utexas.edu/hx659/www/Files/semiparametric_discrete_game_11_29_2012.pdf
    File Function: Revised version, 2012
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peter Kooreman & Adriaan R. Soetevent, 2007. "A discrete-choice model with social interactions: with an application to high school teen behavior," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 599-624.
    2. 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.
    3. Yuanyuan Wan & Haiqing Xu, 2010. "Semiparametric identification and estimation of binary discrete games of incomplete information with correlated private signals," Department of Economics Working Papers 130913, The University of Texas at Austin, Department of Economics.
    4. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    5. Áureo de Paula & Xun Tang, 2012. "Inference of Signs of Interaction Effects in Simultaneous Games With Incomplete Information," Econometrica, Econometric Society, vol. 80(1), pages 143-172, January.
    6. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    7. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
    8. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    9. Aureo de Paula & Xun Tang, 2010. "Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information, Second Version," PIER Working Paper Archive 11-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 12 Feb 2011.
    10. Timothy F. Bresnahan & Peter C. Reiss, 1990. "Entry in Monopoly Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(4), pages 531-553.
    11. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    12. David McAdams, 2003. "Isotone Equilibrium in Games of Incomplete Information," Econometrica, Econometric Society, vol. 71(4), pages 1191-1214, July.
    13. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    14. 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.
    15. Andrew Sweeting, 2009. "The strategic timing incentives of commercial radio stations: An empirical analysis using multiple equilibria," RAND Journal of Economics, RAND Corporation, vol. 40(4), pages 710-742, December.
    16. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    17. Athey, Susan, 2001. "Single Crossing Properties and the Existence of Pure Strategy Equilibria in Games of Incomplete Information," Econometrica, Econometric Society, vol. 69(4), pages 861-889, July.
    18. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    19. Katja Seim, 2006. "An empirical model of firm entry with endogenous product‐type choices," RAND Journal of Economics, RAND Corporation, vol. 37(3), pages 619-640, September.
    20. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
    21. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nianqing Liu & Quang Vuong & Haiqing Xu, 2012. "Rationalization and Identification of Discrete Games with Correlated Types," Department of Economics Working Papers 130915, The University of Texas at Austin, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nianqing Liu & Quang Vuong & Haiqing Xu, 2012. "Rationalization and Identification of Discrete Games with Correlated Types," Department of Economics Working Papers 130915, The University of Texas at Austin, Department of Economics.
    2. Liu, Nianqing & Vuong, Quang & Xu, Haiqing, 2017. "Rationalization and identification of binary games with correlated types," Journal of Econometrics, Elsevier, vol. 201(2), pages 249-268.
    3. Wan, Yuanyuan & Xu, Haiqing, 2014. "Semiparametric identification of binary decision games of incomplete information with correlated private signals," Journal of Econometrics, Elsevier, vol. 182(2), pages 235-246.
    4. Aradillas-Lopez, Andres, 2012. "Pairwise-difference estimation of incomplete information games," Journal of Econometrics, Elsevier, vol. 168(1), pages 120-140.
    5. Yuanyuan Wan & Haiqing Xu, 2010. "Semiparametric identification and estimation of binary discrete games of incomplete information with correlated private signals," Department of Economics Working Papers 130913, The University of Texas at Austin, Department of Economics.
    6. José‐Antonio Espín‐Sánchez & Álvaro Parra & Yuzhou Wang, 2023. "Equilibrium uniqueness in entry games with private information," RAND Journal of Economics, RAND Corporation, vol. 54(3), pages 512-540, September.
    7. Paul B. Ellickson & Sanjog Misra, 2011. "Structural Workshop Paper --Estimating Discrete Games," Marketing Science, INFORMS, vol. 30(6), pages 997-1010, November.
    8. Kline, Brendan, 2015. "Identification of complete information games," Journal of Econometrics, Elsevier, vol. 189(1), pages 117-131.
    9. Luo, Yao & Xiao, Ping & Xiao, Ruli, 2022. "Identification of dynamic games with unobserved heterogeneity and multiple equilibria," Journal of Econometrics, Elsevier, vol. 226(2), pages 343-367.
    10. Yoon, Jangsu, 2024. "Identification and estimation of sequential games of incomplete information with multiple equilibria," Journal of Econometrics, Elsevier, vol. 238(2).
    11. Marcoux, Mathieu, 2022. "Strategic interactions in mobile network investment with a new entrant and unobserved heterogeneity," International Journal of Industrial Organization, Elsevier, vol. 82(C).
    12. Xiao, Ruli, 2018. "Identification and estimation of incomplete information games with multiple equilibria," Journal of Econometrics, Elsevier, vol. 203(2), pages 328-343.
    13. Jos'-Antonio Esp'n-S'nchez & 'lvaro Parra, 2018. "Entry Games under Private Information," Cowles Foundation Discussion Papers 2126, Cowles Foundation for Research in Economics, Yale University.
    14. A. Orhun, 2013. "Spatial differentiation in the supermarket industry: The role of common information," Quantitative Marketing and Economics (QME), Springer, vol. 11(1), pages 3-37, March.
    15. Áureo de Paula & Xun Tang, 2020. "Testable implications of multiple equilibria in discrete games with correlated types," CeMMAP working papers CWP56/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. 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.
    17. Ting Zhu & Vishal Singh, 2009. "Spatial competition with endogenous location choices: An application to discount retailing," Quantitative Marketing and Economics (QME), Springer, vol. 7(1), pages 1-35, March.
    18. Natalia Lazzati & John K.-H. Quah & Koji Shirai, 2018. "Nonparametric analysis of monotone choice," Discussion Paper Series 184, School of Economics, Kwansei Gakuin University.
    19. Mitsukuni Nishida, 2015. "Estimating a Model of Strategic Network Choice: The Convenience-Store Industry in Okinawa," Marketing Science, INFORMS, vol. 34(1), pages 20-38, January.
    20. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.

    More about this item

    Keywords

    Bayesian Nash Equilibrium; Discrete game; Incomplete information; Monotone strategy;
    All these keywords.

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tex:wpaper:130911. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Caroline Thomas (email available below). General contact details of provider: https://edirc.repec.org/data/deutxus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.