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Econometric Analysis of Games with Multiple Equilibria

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  • Áureo de Paula

    (Department of Economics, University College London, London WC1E 6BT, United Kingdom; Center for Microdata Methods and Practice (CeMMAP) and Institute for Fiscal Studies, London WC1E 7AE, United Kingdom)

Abstract

This article reviews the recent literature on the econometric analysis of games in which multiple solutions are possible. Multiplicity does not necessarily preclude the estimation of a particular model (and, in certain cases, even improves its identification), but ignoring it can lead to misspecifications. The review starts with a general characterization of structural models that highlights how multiplicity affects the classical paradigm. Because the information structure is an important guide to identification and estimation strategies, I discuss games of complete and incomplete information separately. Although many of the techniques discussed here can be transported across different information environments, some are specific to particular models. Models of social interactions are also surveyed. I close with a brief discussion of postestimation issues and research prospects.

Suggested Citation

  • Áureo de Paula, 2013. "Econometric Analysis of Games with Multiple Equilibria," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 107-131, May.
    • Handle: RePEc:anr:reveco:v:5:y:2013:p:107-131
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    1. 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.
    2. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    3. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    4. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2009. "Sharp identification regions in models with convex predictions: games, individual choice, and incomplete data," CeMMAP working papers CWP27/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. George J. Mailath, 1998. "Corrigenda [Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory]," Journal of Economic Literature, American Economic Association, vol. 36(4), pages 1941-1941, December.
    6. Andrew Chesher & Adam Rosen, 2012. "Simultaneous equations for discrete outcomes: coherence, completeness, and identification," CeMMAP working papers 21/12, Institute for Fiscal Studies.
    7. Andrea Moro, 2003. "The Effect Of Statistical Discrimination On Black-White Wage Inequality: Estimating A Model With Multiple Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 467-500, May.
    8. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    9. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    10. 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.
    11. Jovanovic, Boyan, 1989. "Observable Implications of Models with Multiple Equilibria," Econometrica, Econometric Society, vol. 57(6), pages 1431-1437, November.
    12. Kline, Brendan, 2015. "Identification of complete information games," Journal of Econometrics, Elsevier, vol. 189(1), pages 117-131.
    13. 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.
    14. Hahn, Jinyong & Moon, Hyungsik Roger, 2010. "Panel Data Models With Finite Number Of Multiple Equilibria," Econometric Theory, Cambridge University Press, vol. 26(3), pages 863-881, June.
    15. Todd, Petra E. & Wolpin, Kenneth I., 2012. "Estimating a Coordination Game in the Classroom," Working Papers 14-017, Rice University, Department of Economics.
    16. George J. Mailath, 1998. "Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory," Journal of Economic Literature, American Economic Association, vol. 36(3), pages 1347-1374, September.
    17. 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.
    18. Bo E. Honor & Áureo De Paula, 2010. "Interdependent Durations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(3), pages 1138-1163.
    19. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    20. Manski, Charles F, 1987. "Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data," Econometrica, Econometric Society, vol. 55(2), pages 357-362, March.
    21. Bresnahan, Timothy F & Reiss, Peter C, 1991. "Entry and Competition in Concentrated Markets," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 977-1009, October.
    22. 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.
    23. Arie Beresteanu, 2009. "Sharp Identification Regions in Models with Convex Predictions: Games, Individual Choice, and Incomplete Data," Working Paper 428, Department of Economics, University of Pittsburgh, revised Sep 2010.
    24. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    25. Daniel A. Ackerberg & Gautam Gowrisankaran, 2006. "Quantifying equilibrium network externalities in the ACH banking industry," RAND Journal of Economics, RAND Corporation, vol. 37(3), pages 738-761, September.
    26. Shakeeb Khan & Elie Tamer, 2010. "Irregular Identification, Support Conditions, and Inverse Weight Estimation," Econometrica, Econometric Society, vol. 78(6), pages 2021-2042, November.
    27. Maximilian Kasy, 2015. "Non‐parametric inference on the number of equilibria," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 1-39, February.
    28. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
    29. 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.
    30. Hyungsik Roger Moon & Frank Schorfheide, 2012. "Bayesian and Frequentist Inference in Partially Identified Models," Econometrica, Econometric Society, vol. 80(2), pages 755-782, March.
    31. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871525, November.
    32. Brock, William A. & Durlauf, Steven N., 2007. "Identification of binary choice models with social interactions," Journal of Econometrics, Elsevier, vol. 140(1), pages 52-75, September.
    33. Alfred Galichon & Marc Henry, 2011. "Set Identification in Models with Multiple Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1264-1298.
    34. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692083, November.
    35. 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.
    36. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    37. Patrick Bajari & Jinyong Hahn & Han Hong & Geert Ridder, 2011. "A Note On Semiparametric Estimation Of Finite Mixtures Of Discrete Choice Models With Application To Game Theoretic Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(3), pages 807-824, August.
    38. de Paula, Áureo, 2009. "Inference in a synchronization game with social interactions," Journal of Econometrics, Elsevier, vol. 148(1), pages 56-71, January.
    39. Federico Echenique & Ivana Komunjer, 2009. "Testing Models With Multiple Equilibria by Quantile Methods," Econometrica, Econometric Society, vol. 77(4), pages 1281-1297, July.
    40. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-318, May.
    41. Peter Hall & Amnon Neeman & Reza Pakyari & Ryan Elmore, 2005. "Nonparametric inference in multivariate mixtures," Biometrika, Biometrika Trust, vol. 92(3), pages 667-678, September.
    42. 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.
    43. repec:oup:restud:v:78:y::i:4:p:1264-1298 is not listed on IDEAS
    44. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
    45. Xiaohong Chen & Elie Tamer & Alexander Torgovitsky, 2011. "Sensitivity Analysis in Semiparametric Likelihood Models," Cowles Foundation Discussion Papers 1836, Cowles Foundation for Research in Economics, Yale University.
    46. Alberto Bisin & Andrea Moro & Giorgio Topa, 2011. "The Empirical Content of Models with Multiple Equilibria in Economies with Social Interactions," NBER Working Papers 17196, National Bureau of Economic Research, Inc.
    47. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    48. 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.
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    More about this item

    Keywords

    identification; multiplicity; social interactions;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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