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Econometric Analysis of Games with Multiple Equilibria


  • 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)


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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    References listed on IDEAS

    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. 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.
    3. 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.
    4. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    5. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    6. 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.
    7. Kline, Brendan, 2015. "Identification of complete information games," Journal of Econometrics, Elsevier, vol. 189(1), pages 117-131.
    8. Hahn, Jinyong & Moon, Hyungsik Roger, 2010. "Panel Data Models With Finite Number Of Multiple Equilibria," Econometric Theory, Cambridge University Press, vol. 26(03), pages 863-881, June.
    9. Todd, Petra E. & Wolpin, Kenneth I., 2012. "Estimating a Coordination Game in the Classroom," Working Papers 14-017, Rice University, Department of Economics.
    10. Bo E. Honor & Áureo De Paula, 2010. "Interdependent Durations," Review of Economic Studies, Oxford University Press, vol. 77(3), pages 1138-1163.
    11. 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.
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    13. Maximilian Kasy, 2015. "Non‐parametric inference on the number of equilibria," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 1-39, February.
    14. 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.
    15. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    16. de Paula, Áureo, 2009. "Inference in a synchronization game with social interactions," Journal of Econometrics, Elsevier, vol. 148(1), pages 56-71, January.
    17. Federico Echenique & Ivana Komunjer, 2009. "Testing Models With Multiple Equilibria by Quantile Methods," Econometrica, Econometric Society, vol. 77(4), pages 1281-1297, July.
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    19. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
    20. 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.
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    Cited by:

    1. Abito, Jose Miguel, 2015. "How much can we identify from repeated games?," MPRA Paper 66378, University Library of Munich, Germany.
    2. Sanchez Villalba, Miguel, 2015. "Global inspection games," Journal of Public Economics, Elsevier, vol. 128(C), pages 59-72.
    3. Arun Advani & Bansi Malde, 2014. "Empirical methods for networks data: social effects, network formation and measurement error," IFS Working Papers W14/34, Institute for Fiscal Studies.
    4. Santiago Pereda Fernández, 2016. "Copula-based random effects models for clustered data," Temi di discussione (Economic working papers) 1092, Bank of Italy, Economic Research and International Relations Area.
    5. Sokbae Lee & Kyungchui (Kevin) Song & Yoon-Jae Whang, 2014. "Testing for a general class of functional inequalities," CeMMAP working papers CWP09/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. José-Alberto Guerra & Myra Mohnen, 2017. "Multinomial choice with social interactions: occupations in Victorian London," DOCUMENTOS CEDE 015667, UNIVERSIDAD DE LOS ANDES-CEDE.
    7. Che-Lin Su, 2014. "Estimating discrete-choice games of incomplete information: Simple static examples," Quantitative Marketing and Economics (QME), Springer, vol. 12(2), pages 167-207, June.
    8. 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.

    More about this item


    identification; multiplicity; social interactions;

    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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