Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/tor/tecipa/tecipa-449.html
   My bibliography  Save this paper

Identification and estimation of dynamic games when players' beliefs are not in equilibrium

Author

Listed:
  • Victor Aguirregabiria
  • Arvind Magesan
Abstract
This paper deals with the identification and estimation of dynamic games when players' beliefs about other players' actions are biased, i.e., beliefs do not represent the probability distribution of the actual behavior of other players conditional on the information available. First, we show that a exclusion restriction, typically used to identify empirical games, provides testable nonparametric restrictions of the null hypothesis of equilibrium beliefs. Second, we prove that this exclusion restriction, together with consistent estimates of beliefs at several points in the support of the special state variable (i.e., the variable involved in the exclusion restriction), is sufficient for nonparametric point-identification of players' payoff and belief functions. The consistent estimates of beliefs at some points of support may come either from an assumption of unbiased beliefs at these points in the state space, or from available data on elicited beliefs for some values of the state variables. Third, we propose a simple two-step estimation method and a sequential generalization of the method that improves its asymptotic and finite sample properties. We illustrate our model and methods using both Monte Carlo experiments and an empirical application of a dynamic game of store location by retail chains. The key conditions for the identification of beliefs and payoffs in our application are the following: (a) the previous year's network of stores of the competitor does not have a direct effect on the profit of a firm, but the firm's own network of stores at previous year does affect its profit because the existence of sunk entry costs and economies of density in these costs; and (b) firms' beliefs are unbiased in those markets that are close, in a geographic sense, to the opponent's network of stores, though beliefs are unrestricted, and potentially biased, for unexplored markets which are farther away from the competitors' network. Our estimates show significant evidence of biased beliefs.

Suggested Citation

  • Victor Aguirregabiria & Arvind Magesan, 2012. "Identification and estimation of dynamic games when players' beliefs are not in equilibrium," Working Papers tecipa-449, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-449
    as

    Download full text from publisher

    File URL: https://www.economics.utoronto.ca/public/workingPapers/tecipa-449.pdf
    File Function: Main Text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. David Besanko & Ulrich Doraszelski, 2004. "Capacity Dynamics and Endogenous Asymmetries in Firm Size," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 23-49, Spring.
    2. Rutström, E. Elisabet & Wilcox, Nathaniel T., 2009. "Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test," Games and Economic Behavior, Elsevier, vol. 67(2), pages 616-632, November.
    3. Otto Toivanen & Michael Waterson, 2005. "Market Structure and Entry: Where's the Beef?," RAND Journal of Economics, The RAND Corporation, vol. 36(3), pages 680-699, Autumn.
    4. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    5. 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.
    6. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    7. Aradillas-Lopez, Andres & Tamer, Elie, 2008. "The Identification Power of Equilibrium in Simple Games," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 261-310.
    8. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    9. Frank Heinemann & Rosemarie Nagel & Peter Ockenfels, 2009. "Measuring Strategic Uncertainty in Coordination Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(1), pages 181-221.
    10. Miguel A. Costa-Gomes & Georg Weizsäcker, 2008. "Stated Beliefs and Play in Normal-Form Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 729-762.
    11. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606.
    12. 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.
    13. Thierry Magnac & David Thesmar, 2002. "Identifying Dynamic Discrete Decision Processes," Econometrica, Econometric Society, vol. 70(2), pages 801-816, March.
    14. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 497-529.
    15. Adeline Delavande, 2008. "Pill, Patch, Or Shot? Subjective Expectations And Birth Control Choice," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(3), pages 999-1042, August.
    16. Junichi Suzuki, 2013. "Land Use Regulation As A Barrier To Entry: Evidence From The Texas Lodging Industry," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(2), pages 495-523, May.
    17. Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
    18. Charles F. Manski, 2004. "Measuring Expectations," Econometrica, Econometric Society, vol. 72(5), pages 1329-1376, September.
    19. Aguirregabiria, Victor, 2010. "Another Look at the Identification of Dynamic Discrete Decision Processes: An Application to Retirement Behavior," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 201-218.
    20. Morris, Stephen & Shin, Hyun Song, 2004. "Coordination risk and the price of debt," European Economic Review, Elsevier, vol. 48(1), pages 133-153, February.
    21. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    22. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, September.
    23. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    24. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    25. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
    26. Palfrey, Thomas R. & Wang, Stephanie W., 2009. "On eliciting beliefs in strategic games," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 98-109, August.
    27. 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.
    28. Aguirregabiria, Victor, 2008. "Comment: The Identification Power of Equilibrium in Simple Games," MPRA Paper 15987, University Library of Munich, Germany.
    29. Rosa L. Matzkin, 1988. "Nonparametric and Distribution-Free Estimation of the Binary Choice and the Threshold-Crossing Models," Cowles Foundation Discussion Papers 889, Cowles Foundation for Research in Economics, Yale University.
    30. Crawford, Vincent P & Haller, Hans, 1990. "Learning How to Cooperate: Optimal Play in Repeated Coordination Games," Econometrica, Econometric Society, vol. 58(3), pages 571-595, May.
    31. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    32. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590.
    33. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(1), pages 147-165.
    34. Matzkin, Rosa L, 1992. "Nonparametric and Distribution-Free Estimation of the Binary Threshold Crossing and the Binary Choice Models," Econometrica, Econometric Society, vol. 60(2), pages 239-270, March.
    35. A. Norets & X. Tang, 2014. "Semiparametric Inference in Dynamic Binary Choice Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(3), pages 1229-1262.
    36. Michael J. Mazzeo, 2002. "Product Choice and Oligopoly Market Structure," RAND Journal of Economics, The RAND Corporation, vol. 33(2), pages 221-242, Summer.
    37. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    38. Andriy Norets & Xun Tang, 2010. "Semiparametric Inference in Dynamic Binary Choice Models, Second Version," PIER Working Paper Archive 12-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 17 Apr 2012.
    39. Paul Ellickson & Beresteanu Arie, 2005. "The Dynamics of Retail Oligopolies," 2005 Meeting Papers 829, Society for Economic Dynamics.
    40. van der Klaauw, Wilbert & Wolpin, Kenneth I., 2008. "Social security and the retirement and savings behavior of low-income households," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 21-42, July.
    41. Yingyao Hu & Matthew Shum, 2008. "Identifying Dynamic Games with Serially-Correlated Unobservables," Economics Working Paper Archive 546, The Johns Hopkins University,Department of Economics.
    42. 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.
    43. Aradillas-Lopez, Andres, 2012. "Pairwise-difference estimation of incomplete information games," Journal of Econometrics, Elsevier, vol. 168(1), pages 120-140.
    44. Besanko, David & Doraszelski, Ulrich & Lu, Lauren Xiaoyuan & Satterthwaite, Mark, 2010. "On the role of demand and strategic uncertainty in capacity investment and disinvestment dynamics," International Journal of Industrial Organization, Elsevier, vol. 28(4), pages 383-389, July.
    45. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    46. Avi Goldfarb & Mo Xiao, 2011. "Who Thinks about the Competition? Managerial Ability and Strategic Entry in US Local Telephone Markets," American Economic Review, American Economic Association, vol. 101(7), pages 3130-3161, December.
    47. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, January.
    48. Martin Pesendorfer & Philipp Schmidt-Dengler, 2008. "Asymptotic Least Squares Estimators for Dynamic Games -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 901-928.
    49. 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.
    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. Paul S. Koh, 2022. "Stable Outcomes and Information in Games: An Empirical Framework," Papers 2205.04990, arXiv.org, revised May 2023.
    2. Federico A. Bugni & Jackson Bunting & Takuya Ura, 2020. "Testing homogeneity in dynamic discrete games in finite samples," Papers 2010.02297, arXiv.org, revised Aug 2024.
    3. Tobias Salz & Emanuel Vespa, 2020. "Estimating dynamic games of oligopolistic competition: an experimental investigation," RAND Journal of Economics, RAND Corporation, vol. 51(2), pages 447-469, June.
    4. Victor Aguirregabiria & Mathieu Marcoux, 2021. "Imposing equilibrium restrictions in the estimation of dynamic discrete games," Quantitative Economics, Econometric Society, vol. 12(4), pages 1223-1271, November.
    5. Victor Aguirregabiria, 2021. "Identification of firms’ beliefs in structural models of market competition," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 54(1), pages 5-33, February.
    6. Jackson Bunting & Takuya Ura, 2023. "Faster estimation of dynamic discrete choice models using index invertibility," Papers 2304.02171, arXiv.org, revised Jul 2024.
    7. An, Yonghong & Hu, Yingyao & Xiao, Ruli, 2021. "Dynamic decisions under subjective expectations: A structural analysis," Journal of Econometrics, Elsevier, vol. 222(1), pages 645-675.
    8. Victor Aguirregabiria & Jihye Jeon, 2020. "Firms’ Beliefs and Learning: Models, Identification, and Empirical Evidence," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 56(2), pages 203-235, March.
    9. Victor Aguirregabiria & Francis Guiton, 2022. "Decentralized Decision-Making in Retail Chains: Evidence from Inventory Management," Working Papers tecipa-722, University of Toronto, Department of Economics.
    10. Waterson, Michael & Toivanen, Otto, 2011. "Retail Chain Expansion: The Early Years of McDonalds in Great Britain," CEPR Discussion Papers 8534, C.E.P.R. Discussion Papers.
    11. Alexandra Belova & Philippe Gagnepain & Stéphane Gauthier, 2020. "An assessment of Nash equilibria in the airline industry," Working Papers halshs-02932780, HAL.
    12. Aguirregabiria, Victor & Xie, Erhao, 2016. "Identification of Biased Beliefs in Games of Incomplete Information Using Experimental Data," CEPR Discussion Papers 11275, C.E.P.R. Discussion Papers.
    13. Taiga Tsubota, 2021. "Identifying Dynamic Discrete Choice Models with Hyperbolic Discounting," Papers 2111.10721, arXiv.org, revised Oct 2024.
    14. Ron Borkovsky & Paul Ellickson & Brett Gordon & Victor Aguirregabiria & Pedro Gardete & Paul Grieco & Todd Gureckis & Teck-Hua Ho & Laurent Mathevet & Andrew Sweeting, 2015. "Multiplicity of equilibria and information structures in empirical games: challenges and prospects," Marketing Letters, Springer, vol. 26(2), pages 115-125, June.
    15. Kojevnikov, Denis & Song, Kyungchul, 2023. "Econometric inference on a large Bayesian game with heterogeneous beliefs," Journal of Econometrics, Elsevier, vol. 237(1).
    16. Ali Hortacsu & Olivia R. Natan & Hayden Parsley & Timothy Schwieg & Kevin R. Williams, 2021. "Organizational Structure and Pricing: Evidence from a Large U.S. Airline," Cowles Foundation Discussion Papers 2312R4, Cowles Foundation for Research in Economics, Yale University, revised Jun 2023.
    17. Lorenzo Magnolfi & Camilla Roncoroni, 2023. "Estimation of Discrete Games with Weak Assumptions on Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(4), pages 2006-2041.
    18. Erhao Xie, 2018. "Inference in Games Without Nash Equilibrium: An Application to Restaurants, Competition in Opening Hours," Staff Working Papers 18-60, Bank of Canada.
    19. Taisuke Otsu & Martin Pesendorfer, 2021. "Equilibrium multiplicity in dynamic games: testing and estimation," STICERD - Econometrics Paper Series 618, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    20. Avi Goldfarb & Teck-Hua Ho & Wilfred Amaldoss & Alexander Brown & Yan Chen & Tony Cui & Alberto Galasso & Tanjim Hossain & Ming Hsu & Noah Lim & Mo Xiao & Botao Yang, 2012. "Behavioral models of managerial decision-making," Marketing Letters, Springer, vol. 23(2), pages 405-421, June.
    21. Kojevnikov, Denis & Song, Kyungchul, 2023. "Econometric inference on a large bayesian game with heterogeneous beliefs," Other publications TiSEM aca0631e-4f8a-45c7-af3a-4, Tilburg University, School of Economics and Management.
    22. Koh, Paul S., 2023. "Stable outcomes and information in games: An empirical framework," Journal of Econometrics, Elsevier, vol. 237(1).

    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. Erhao Xie, 2018. "Inference in Games Without Nash Equilibrium: An Application to Restaurants, Competition in Opening Hours," Staff Working Papers 18-60, Bank of Canada.
    2. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    3. Victor Aguirregabiria & Victor Aguirregabiria & Aviv Nevo & Aviv Nevo, 2010. "Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games," Working Papers tecipa-419, University of Toronto, Department of Economics.
    4. Paul B. Ellickson & Sanjog Misra, 2011. "Structural Workshop Paper --Estimating Discrete Games," Marketing Science, INFORMS, vol. 30(6), pages 997-1010, November.
    5. Arcidiacono, Peter & Miller, Robert A., 2020. "Identifying dynamic discrete choice models off short panels," Journal of Econometrics, Elsevier, vol. 215(2), pages 473-485.
    6. Yoon, Jangsu, 2024. "Identification and estimation of sequential games of incomplete information with multiple equilibria," Journal of Econometrics, Elsevier, vol. 238(2).
    7. 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.
    8. Aradillas-Lopez, Andres, 2012. "Pairwise-difference estimation of incomplete information games," Journal of Econometrics, Elsevier, vol. 168(1), pages 120-140.
    9. A. Ronald Gallant & Han Hong & Ahmed Khwaja, 2018. "The Dynamic Spillovers of Entry: An Application to the Generic Drug Industry," Management Science, INFORMS, vol. 64(3), pages 1189-1211, March.
    10. 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.
    11. Jason R. Blevins & Ahmed Khwaja & Nathan Yang, 2018. "Firm Expansion, Size Spillovers, and Market Dominance in Retail Chain Dynamics," Management Science, INFORMS, vol. 64(9), pages 4070-4093.
    12. Steven T Berry & Giovanni Compiani, 2023. "An Instrumental Variable Approach to Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(4), pages 1724-1758.
    13. Hanming Fang & Yang Wang, 2015. "Estimating Dynamic Discrete Choice Models With Hyperbolic Discounting, With An Application To Mammography Decisions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(2), pages 565-596, May.
    14. Aguirregabiria, Victor & Xie, Erhao, 2016. "Identification of Biased Beliefs in Games of Incomplete Information Using Experimental Data," CEPR Discussion Papers 11275, C.E.P.R. Discussion Papers.
    15. Victor Aguirregabiria, 2021. "Identification of firms’ beliefs in structural models of market competition," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 54(1), pages 5-33, February.
    16. Victor Aguirregabiria & Jihye Jeon, 2020. "Firms’ Beliefs and Learning: Models, Identification, and Empirical Evidence," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 56(2), pages 203-235, March.
    17. Michaela Draganska & Sanjog Misra & Victor Aguirregabiria & Pat Bajari & Liran Einav & Paul Ellickson & Dan Horsky & Sridhar Narayanan & Yesim Orhun & Peter Reiss & Katja Seim & Vishal Singh & Raphael, 2008. "Discrete choice models of firms’ strategic decisions," Marketing Letters, Springer, vol. 19(3), pages 399-416, December.
    18. Sumon Datta & K. Sudhir, 2013. "Does reducing spatial differentiation increase product differentiation? Effects of zoning on retail entry and format variety," Quantitative Marketing and Economics (QME), Springer, vol. 11(1), pages 83-116, March.
    19. Otero, Karina V., 2016. "Nonparametric identification of dynamic multinomial choice games: unknown payoffs and shocks without interchangeability," MPRA Paper 86784, University Library of Munich, Germany.
    20. Sumon Datta & K. Sudhir, 2013. "Does reducing spatial differentiation increase product differentiation? Effects of zoning on retail entry and format variety," Quantitative Marketing and Economics (QME), Springer, vol. 11(1), pages 83-116, March.

    More about this item

    Keywords

    Dynamic games; Rational behavior; Rationalizability; Identification; Estimation; Market entry-exit.;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    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:tor:tecipa:tecipa-449. 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: RePEc Maintainer (email available below). General contact details of provider: .

    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.