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Rationalization and identification of binary games with correlated types

Author

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  • Liu, Nianqing
  • Vuong, Quang
  • Xu, Haiqing
Abstract
This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for type correlation is crucial in global games and in models with social interactions as it represents correlated private information and homophily, respectively. Our approach is fully nonparametric in the joint distribution of types and the strategic effects in the payoffs. First, under monotone pure Bayesian Nash Equilibrium strategy, we characterize all the restrictions if any on the distribution of players’ choices imposed by the game-theoretic model as well as restrictions associated with two assumptions frequently made in the empirical analysis of discrete games. Namely, we consider exogeneity of payoff shifters relative to private information, and mutual independence of private information given payoff shifters. Second, we study the nonparametric identification of the payoff functions and types distribution. We show that the model with exogenous payoff shifters is fully identified up to a single location-scale normalization under some exclusion restrictions and rank conditions. Third, we discuss partial identification under weaker conditions and multiple equilibria. Lastly, we briefly point out the implications of our results for model testing and estimation.

Suggested Citation

  • Liu, Nianqing & Vuong, Quang & Xu, Haiqing, 2017. "Rationalization and identification of binary games with correlated types," Journal of Econometrics, Elsevier, vol. 201(2), pages 249-268.
    • Handle: RePEc:eee:econom:v:201:y:2017:i:2:p:249-268
    DOI: 10.1016/j.jeconom.2017.08.007
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    Cited by:

    1. Rongyu Wang, 2024. "Strategic Entry with Correlated Private Information," Journal of Interdisciplinary Economics, , vol. 36(2), pages 133-165, July.
    2. Erhao Xie, 2022. "Nonparametric Identification of Incomplete Information Discrete Games with Non-equilibrium Behaviors," Staff Working Papers 22-22, Bank of Canada.
    3. Emmanuel Guerre & Yao Luo, 2019. "Nonparametric Identification of First-Price Auction with Unobserved Competition: A Density Discontinuity Framework," Papers 1908.05476, arXiv.org, revised Jan 2022.

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    More about this item

    Keywords

    Rationalization; Identification; Discrete game; Social interactions; Global games;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

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