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Bounds for best response functions in binary games

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  • Kline, Brendan
  • Tamer, Elie

Abstract

This paper studies the identification of best response functions in binary games without making strong parametric assumptions about the payoffs. The best response function gives the utility maximizing response to a decision of the other players. This is analogous to the response function in the treatment–response literature, taking the decision of the other players as the treatment, except that the best response function has additional structure implied by the associated utility maximization problem. Further, the relationship between the data and the best response function is not the same as the relationship between the data and the response function in the treatment–response literature. We focus especially on the case of a complete information entry game with two firms. We also discuss the case of an entry game with many firms, non-entry games, and incomplete information. Our analysis of the entry game is based on the observation of realized entry decisions, which we then link to the best response functions under various assumptions including those concerning the level of rationality of the firms, including the assumption of Nash equilibrium play, the symmetry of the payoffs between firms, and whether mixed strategies are admitted.

Suggested Citation

  • Kline, Brendan & Tamer, Elie, 2012. "Bounds for best response functions in binary games," Journal of Econometrics, Elsevier, vol. 166(1), pages 92-105.
    • Handle: RePEc:eee:econom:v:166:y:2012:i:1:p:92-105
    DOI: 10.1016/j.jeconom.2011.06.008
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    Citations

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    Cited by:

    1. Matthew A. Masten & Alexandre Poirier, 2018. "Interpreting Quantile Independence," Papers 1804.10957, arXiv.org.
    2. Natalia Lazzati & John K.-H. Quah & Koji Shirai, 2015. "A revealed preference theory of monotone choice and strategic complementarity," Discussion Paper Series 138, School of Economics, Kwansei Gakuin University, revised Dec 2015.
    3. Brendan Kline & Elie Tamer, 2024. "Counterfactual Analysis in Empirical Games," Papers 2410.12731, arXiv.org.
    4. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2013. "Random coefficients in static games of complete information," CeMMAP working papers CWP12/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Barkley, Aaron & Groeger, Joachim R. & Miller, Robert A., 2021. "Bidding frictions in ascending auctions," Journal of Econometrics, Elsevier, vol. 223(2), pages 376-400.
    6. Kline, Brendan, 2015. "Identification of complete information games," Journal of Econometrics, Elsevier, vol. 189(1), pages 117-131.
    7. Francesca Molinari, 2020. "Microeconometrics with Partial Identification," Papers 2004.11751, arXiv.org.
    8. Brendan Kline & Elie Tamer, 2016. "Bayesian inference in a class of partially identified models," Quantitative Economics, Econometric Society, vol. 7(2), pages 329-366, July.
    9. Andrew Chesher & Adam Rosen, 2012. "Simultaneous equations for discrete outcomes: coherence, completeness, and identification," CeMMAP working papers CWP21/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Jun, Sung Jae & Pinkse, Joris, 2020. "Counterfactual prediction in complete information games: Point prediction under partial identification," Journal of Econometrics, Elsevier, vol. 216(2), pages 394-429.
    11. Marc HENRY & Ismael MOURIFIÉ, 2013. "Nonparametric Sharp Bounds For Payoffs In 2 × 2 Games," Working Papers tecipa-500, University of Toronto, Department of Economics.
    12. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. 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.
    14. Jiayu Huang & Yifan Wang & Yaojun Fan & Hexuan Li, 2022. "Gauging the effect of investor overconfidence on trading volume from the perspective of the relationship between lagged stock returns and current trading volume," International Finance, Wiley Blackwell, vol. 25(1), pages 103-123, April.
    15. Dunker, Fabian & Hoderlein, Stefan & Kaido, Hiroaki & Sherman, Robert, 2018. "Nonparametric identification of the distribution of random coefficients in binary response static games of complete information," Journal of Econometrics, Elsevier, vol. 206(1), pages 83-102.

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    More about this item

    Keywords

    Binary games; Entry games; Best response functions; Multiple equilibria; Mixed strategies; Nash equilibrium; Levels of rationality; Treatment effects; Peer effects;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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