1932

Abstract

This article reviews the econometrics of static games, with a focus on discrete-choice cases. These models have been used to study a rich variety of empirical problems, ranging from labor force participation to entry decisions. We outline the components of a general game and describe the problem of doing robust inference in the presence of multiple solutions, as well as the different econometric approaches that have been applied to tackle this problem. We then describe the specific challenges that arise in different variations of these models depending on whether players are assumed to have complete or incomplete information, as well as whether or not nonequilibrium play is allowed. We describe the results in 2 × 2 games (the most widely studied games in econometrics), and we present extensions and recent results in games with richer action spaces. Areas for future research are also discussed.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-economics-081919-113720
2020-08-02
2024-04-19
Loading full text...

Full text loading...

/deliver/fulltext/economics/12/1/annurev-economics-081919-113720.html?itemId=/content/journals/10.1146/annurev-economics-081919-113720&mimeType=html&fmt=ahah

Literature Cited

  1. Ackerberg D, Gowrisankaran G. 2006. Quantifying equilibrium network externalities in the ACH banking industry. RAND J. Econ. 37:738–61
    [Google Scholar]
  2. Aguirregabiria V, Mira P. 2007. Sequential estimation of dynamic discrete games. Econometrica 75:1–53
    [Google Scholar]
  3. Ahn H. 1995. Nonparametric two-stage estimation of conditional choice probabilities in a binary choice model under uncertainty. J. Econom. 67:337–78
    [Google Scholar]
  4. Ahn H, Manski C. 1993. Distribution theory for the analysis of binary choice under uncertainty with nonparametric estimation of expectations. J. Econom. 56:291–321
    [Google Scholar]
  5. Andrews DWK, Jia-Barwick P. 2010. Inference for parameters defined by moment inequalities. Econometrica 80:2805–26
    [Google Scholar]
  6. Andrews DWK, Shi X. 2013. Inference for parameters defined by conditional moment inequalities. Econometrica 81:609–66
    [Google Scholar]
  7. Andrews DWK, Soares G. 2010. Inference for parameters defined by moment inequalities using generalized moment selection. Econometrica 78:119–57
    [Google Scholar]
  8. Aradillas-López A. 2010. Semiparametric estimation of a simultaneous game with incomplete information. J. Econom. 157:409–31
    [Google Scholar]
  9. Aradillas-López A. 2011. Nonparametric probability bounds for Nash equilibrium actions in a simultaneous discrete game. Quant. Econ. 2:135–71
    [Google Scholar]
  10. Aradillas-López A. 2012. Pairwise difference estimation of incomplete information games. J. Econom. 168:120–40
    [Google Scholar]
  11. Aradillas-López A. 2019. Nonparametric tests for strategic interaction effects with rationalizability. Econ. Lett. 181:149–53
    [Google Scholar]
  12. Aradillas-López A, Gandhi A. 2016. Estimation of games with ordered actions: an application to chain-store entry. Quant. Econ. 7:727–80
    [Google Scholar]
  13. Aradillas-López A, Rosen A. 2019. Inference in ordered response games with complete information Work. Pap., Pa. State Univ., University Park PA:
  14. Aradillas-López A, Tamer E. 2008. The identification power of equilibrium in simple games. J. Bus. Econ. Stat. 26:261–310
    [Google Scholar]
  15. Armstrong TB. 2014. Weighted KS statistics for inference on conditional moment inequalities. J. Econom. 181:92–116
    [Google Scholar]
  16. Armstrong TB. 2015. Asymptotically exact inference in conditional moment inequality models. J. Econom. 186:51–65
    [Google Scholar]
  17. Bajari P, Benkard L, Levin J 2007. Estimating dynamic models of imperfect competition. Econometrica 75:1331–70
    [Google Scholar]
  18. Bajari P, Hong H, Krainer J, Nekipelov D 2010a. Estimating static models of strategic interaction. J. Bus. Econ. Stat. 28:469–82
    [Google Scholar]
  19. Bajari P, Hong H, Ryan SP 2010b. Identification and estimation of discrete games of complete information. Econometrica 78:1529–68
    [Google Scholar]
  20. Beresteanu A, Molchanov I, Molinari F 2011. Sharp identification regions in models with convex moment predictions. Econometrica 79:1785–821
    [Google Scholar]
  21. Beresteanu A, Molinari F. 2008. Asymptotic properties for a class of partially identified models. Econometrica 76:763–814
    [Google Scholar]
  22. Bernheim D. 1984. Rationalizable strategic behavior. Econometrica 52:1007–28
    [Google Scholar]
  23. Berry S. 1992. Estimation of a model of entry in the airline industry. Econometrica 60:889–917
    [Google Scholar]
  24. Berry S, Reiss P. 2007. Empirical models of entry and market structure. The Handbook of Industrial Organization 3 M Armstrong, P Rob 1845–86 Amsterdam: North-Holland
    [Google Scholar]
  25. Berry S, Tamer E. 2007. Identification in models of oligopoly entry. Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress 2 R Blundell, W Newey, T Persson 46–85 Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  26. Bjorn P, Vuong Q. 1984. Simultaneous equations models for dummy endogenous variables: a game theoretic formulation with an application to labor force participation Soc. Sci. Work. Pap. 537, Calif. Inst. Technol. Pasadena, CA:
  27. Bresnahan TF, Reiss PJ. 1990. Entry in monopoly markets. Rev. Econ. Stud. 57:531–53
    [Google Scholar]
  28. Bresnahan TF, Reiss PJ. 1991a. Empirical models of discrete games. J. Econom. 48:57–81
    [Google Scholar]
  29. Bresnahan TF, Reiss PJ. 1991b. Entry and competition in concentrated markets. J. Political Econ. 99:977–1009
    [Google Scholar]
  30. Bugni F. 2010. Bootstrap inference for partially identified models defined by moment inequalities: coverage of the identified set. Econometrica 78:735–53
    [Google Scholar]
  31. Camerer C. 2004. A cognitive hierarchy model of games. Q. J. Econ. 119:861–98
    [Google Scholar]
  32. Chernozhukov V, Hong H, Tamer E 2007. Estimation and confidence regions for parameter sets in econometric models. Econometrica 75:1243–84
    [Google Scholar]
  33. Chernozhukov V, Lee S, Rosen A 2013. Intersection bounds, estimation and inference. Econometrica 81:667–737
    [Google Scholar]
  34. Chesher A, Rosen A. 2017. Generalized instrumental variable models. Econometrica 85:959–89
    [Google Scholar]
  35. Chetverikov D. 2012. Adaptive test of conditional moment inequalities Work. Pap., Mass. Inst. Technol. Cambridge, MA:
  36. Ciliberto F, Tamer E. 2009. Market structure and multiple equilibria in airline markets. Econometrica 77:1791–828
    [Google Scholar]
  37. Costa-Gomes M, Crawford V. 2001. Cognition and behavior in normal-form games: an experimental study. Econometrica 69:1193–235
    [Google Scholar]
  38. Costa-Gomes M, Crawford V. 2006. Cognition and behavior in two-person guessing games: an experimental study. Am. Econ. Rev. 96:1737–68
    [Google Scholar]
  39. Davis P. 2006. Estimation of quantity games in the presence of indivisibilities and heterogeneous firms. J. Econom. 134:187–214
    [Google Scholar]
  40. de Paula A. 2013. Econometric analysis of games with multiple equilibria. Annu. Rev. Econ. 5:107–31
    [Google Scholar]
  41. de Paula A, Tang X 2012. Inference of signs of interaction effects in simultaneous games with incomplete information. Econometrica 80:143–72
    [Google Scholar]
  42. Gale D, Nikaido H. 1965. The Jacobian matrix and the global univalence of mappings. Math. Ann. 159:81–93
    [Google Scholar]
  43. Galichon A, Henry M. 2011. Set identification in models with multiple equilibria. Rev. Econ. Stud. 78:1264–98
    [Google Scholar]
  44. Grieco P. 2014. Discrete games with flexible information structures: an application to local grocery markets. RAND J. Econ. 45:303–40
    [Google Scholar]
  45. Hahn J, Moon H, Snider C 2017. LM test of neglected correlated random effects and its application. J. Bus. Econ. Stat. 35:359–70
    [Google Scholar]
  46. Hansen L, Sargent T. 2016. Robustness Princeton, NJ: Princeton Univ. Press
  47. Heckman JJ. 1978. Dummy endogenous variables in a simultaneous equation system. Econometrica 46:931–59
    [Google Scholar]
  48. Ichimura H. 1993. Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. J. Econom. 58:71–120
    [Google Scholar]
  49. Imbens G, Manski C. 2004. Confidence intervals for partially identified parameters. Econometrica 72:1845–57
    [Google Scholar]
  50. Jovanovic B. 1989. Observable implications of models with multiple equilibria. Econometrica 57:1431–37
    [Google Scholar]
  51. Kaido H, Molinari F, Stoye J 2019. Confidence intervals for projections of partially identified parameters. Econometrica 87:1397–432
    [Google Scholar]
  52. Klein R, Spady R. 1993. An efficient semiparametric estimator for binary response models. Econometrica 61:387–421
    [Google Scholar]
  53. Kline B. 2015. Identification of complete information games. J. Econom. 189:117–31
    [Google Scholar]
  54. Kline B. 2016. The empirical content of games with bounded regressors. Quant. Econ. 7:37–81
    [Google Scholar]
  55. Kline B. 2018. An empirical model of non-equilibrium behavior in games. Quant. Econ. 9:141–81
    [Google Scholar]
  56. Kline B, Tamer E. 2012. Bounds for best response functions in binary games. J. Econom. 166:92–105
    [Google Scholar]
  57. Kline B, Tamer E. 2016. Bayesian inference in a class of partially identified models. Quant. Econ. 7:329–66
    [Google Scholar]
  58. Kosenkova L. 2019. Nonparametric inference in asymmetric first-price auctions with k-rationalizable beliefs Work. Pap., Univ. Va. Charlottesville:
  59. Lewbel A, Tang X. 2015. Identification and estimation of games with incomplete information using excluded regressors. J. Econom. 189:229–44
    [Google Scholar]
  60. Liu N, Xu H, Vuong Q 2017. Rationalization and identification of discrete games with correlated types. J. Econom. 201:249–68
    [Google Scholar]
  61. Marcoux M. 2018. Sharp test for equilibrium uniqueness in discrete games with a flexible information structure Work. Pap., Cent. Interuniv. Rech. Econ. Quant. (CIREQ) Montreal, Can.:
  62. Morris S, Shin H. 2003. Global games: theory and applications. Advances in Economics and Econometrics Theory and Applications, Eighth World Congress 1 M Dewatripont, L Hansen, S Turbovsky 56–114 Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  63. Otsu T, Pesendorfer M, Takahashi Y 2016. Pooling data across markets in dynamic Markov games. Quant. Econ. 7:523–59
    [Google Scholar]
  64. Pakes A, Ostrovsky O, Berry S 2007. Simple estimators for the parameters of discrete dynamic games (with entry/exit examples). RAND J. Econ. 38:373–99
    [Google Scholar]
  65. Pakes A, Porter J, Ho K, Ishii J 2015. Moment inequalities and their application. Econometrica 83:315–34
    [Google Scholar]
  66. Pearce D. 1984. Rationalizable strategic behavior and the problem of perfection. Econometrica 52:1029–50
    [Google Scholar]
  67. Pesendorfer M, Schmidt-Dengler P. 2008. Asymptotic least squares estimators for dynamic games. Rev. Econ. Stud. 75:901–28
    [Google Scholar]
  68. Powell J, Stock J, Stoker T 1989. Semiparametric estimation of index coefficients. Econometrica 57:1403–30
    [Google Scholar]
  69. Romano J, Shaikh A. 2010. Inference for the identified set in partially identified econometric models. Econometrica 78:169–211
    [Google Scholar]
  70. Romano J, Shaikh A, Wolf M 2014. A practical two-step method for testing moment inequalities. Econometrica 82:1979–2002
    [Google Scholar]
  71. Seim K. 2006. An empirical model of firm entry with endogenous product-type choices. RAND J. Econ.37
    [Google Scholar]
  72. Stahl D, Wilson P. 1994. Experimental evidence on players' models of other players. J. Econ. Behav. Organ. 25:309–27
    [Google Scholar]
  73. Stoye J. 2009. More on confidence intervals for partially identified parameters. Econometrica 77:1299–315
    [Google Scholar]
  74. Sweeting A. 2009. The strategic timing of radio commercials: an empirical analysis using multiple equilibria. RAND J. Econ. 40:710–24
    [Google Scholar]
  75. Tamer E. 2003. Incomplete simultaneous discrete response model with multiple equilibria. Rev. Econ. Stud. 70:147–67
    [Google Scholar]
  76. Topkis DM. 1998. Supermodularity and Complementarity Princeton, NJ: Princeton Univ. Press
  77. Torgovitsky A. 2019. Partial identification by extending subdistributions. Quant. Econ. 10:105–44
    [Google Scholar]
  78. Vives X. 1999. Oligopoly Pricing Cambridge, MA: MIT Press
  79. Xiao R. 2018. Identification and estimation of incomplete information games with multiple equilibria. J. Econom. 203:328–43
    [Google Scholar]
  80. Xu H. 2014. Estimation of discrete games with correlated types. Econom. J. 17:241–70
    [Google Scholar]
  81. Xu H, Wan Y. 2014. Semiparametric identification of binary decision games of incomplete information with correlated private signals. J. Econom. 182:235–46
    [Google Scholar]
/content/journals/10.1146/annurev-economics-081919-113720
Loading
/content/journals/10.1146/annurev-economics-081919-113720
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error