IDEAS home Printed from https://ideas.repec.org/p/swe/wpaper/2010-22.html
   My bibliography  Save this paper

Estimation of Finite Sequential Games

Author

Listed:
  • Shiko Maruyama

    () (School of Economics, University of New South Wales)

Abstract

I study the estimation of finite sequential games with perfect information. The major challenge in estimation is computation of high-dimensional truncated integration whose domain is complicated by strategic interaction. I show that this complication resolves when unobserved off-the-equilibrium-path strategies are controlled for. Separately evaluating the likelihood contribution of each subgame perfect strategy profile that rationalizes the observed outcome allows the use of the GHK simulator, the most widely used importance-sampling probit simulator. Monte Carlo experiments demonstrate the performance and robustness of the proposed method, and confirm that misspecification of the decision order leads to underestimation of strategic effect.

Suggested Citation

  • Shiko Maruyama, 2010. "Estimation of Finite Sequential Games," Discussion Papers 2010-22, School of Economics, The University of New South Wales.
  • Handle: RePEc:swe:wpaper:2010-22
    as

    Download full text from publisher

    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2010-22.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. James Andreoni & Emily Blanchard, 2006. "Testing subgame perfection apart from fairness in ultimatum games," Experimental Economics, Springer;Economic Science Association, vol. 9(4), pages 307-321, December.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    3. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
    4. McFadden, Daniel & Ruud, Paul A, 1994. "Estimation by Simulation," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 591-608, November.
    5. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    6. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    7. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
    8. Kempf, Hubert & Rota-Graziosi, Grégoire, 2010. "Endogenizing leadership in tax competition," Journal of Public Economics, Elsevier, vol. 94(9-10), pages 768-776, October.
    9. Geweke, John & Keane, Michael P & Runkle, David, 1994. "Alternative Computational Approaches to Inference in the Multinomial Probit Model," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 609-632, November.
    10. Hajivassiliou, V A, 1994. "A Simulation Estimation Analysis of the External Debt Crises of Developing Countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(2), pages 109-131, April-Jun.
    11. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 497-529.
    12. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    13. Carlos Pimienta & Cristian Litan, 2008. "Conditions for equivalence between sequentiality and subgame perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 539-553, June.
    14. repec:wly:quante:v:8:y:2017:i:1:p:277-316 is not listed on IDEAS
    15. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
    16. Borsch-Supan, Axel & Hajivassiliou, Vassilis A., 1993. "Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models," Journal of Econometrics, Elsevier, vol. 58(3), pages 347-368, August.
    17. Hubert Kempf & Grégoire Rota-Graziosi, 2010. "Endogenizing leadership in the tax competition race," Documents de travail du Centre d'Economie de la Sorbonne 10039, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    18. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    19. Kooreman, Peter, 1994. "Estimation of Econometric Models of Some Discrete Games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(3), pages 255-268, July-Sept.
    20. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    21. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
    22. Sandor, Zsolt & Andras, P.Peter, 2004. "Alternative sampling methods for estimating multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 120(2), pages 207-234, June.
    23. Kai A. Konrad & Harald Künemund & Kjell Erik Lommerud & Julio R. Robledo, 2002. "Geography of the Family," American Economic Review, American Economic Association, vol. 92(4), pages 981-998, September.
    24. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, vol. 66(4), pages 863-896, July.
    25. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
    26. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, August.
    27. Shiko Maruyama & Meliyanni Johar, 2017. "Do siblings free‐ride in “being there” for parents?," Quantitative Economics, Econometric Society, vol. 8(1), pages 277-316, March.
    28. Liesenfeld, Roman & Richard, Jean-François, 2010. "Efficient estimation of probit models with correlated errors," Journal of Econometrics, Elsevier, vol. 156(2), pages 367-376, June.
    29. Michael J. Mazzeo, 2002. "Product Choice and Oligopoly Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 33(2), pages 221-242, Summer.
    30. Shiko Maruyama, 2011. "SOCIALLY OPTIMAL SUBSIDIES FOR ENTRY: THE CASE OF MEDICARE PAYMENTS TO HMOs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 105-129, February.
    31. Zhiyang Jia, 2005. "Labor Supply of Retiring Couples and Heterogeneity in Household Decision-Making Structure," Review of Economics of the Household, Springer, vol. 3(2), pages 215-233, June.
    32. Panle Jia, 2008. "What Happens When Wal-Mart Comes to Town: An Empirical Analysis of the Discount Retailing Industry," Econometrica, Econometric Society, vol. 76(6), pages 1263-1316, November.
    33. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    34. Bas, Muhammet Ali & Signorino, Curtis S. & Walker, Robert W., 2008. "Statistical Backwards Induction: A Simple Method for Estimating Recursive Strategic Models," Political Analysis, Cambridge University Press, vol. 16(01), pages 21-40, December.
    35. 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. Meliyanni Johar & Shiko Maruyama, 2012. "Externality and Strategic Interaction in the Location Choice of Siblings under Altruism toward Parents," Working Papers 201201, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.
    2. repec:wly:quante:v:8:y:2017:i:1:p:277-316 is not listed on IDEAS
    3. Shiko Maruyama & Meliyanni Johar, 2017. "Do siblings free‐ride in “being there” for parents?," Quantitative Economics, Econometric Society, vol. 8(1), pages 277-316, March.

    More about this item

    Keywords

    Inference In Discrete Games; Sequential Games; Monte Carlo Integration; GHK Simulator; Subgame Perfection; Perfect Information;

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:swe:wpaper:2010-22. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Hongyi Li). General contact details of provider: http://edirc.repec.org/data/senswau.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.