IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2205.04990.html
   My bibliography  Save this paper

Stable Outcomes and Information in Games: An Empirical Framework

Author

Listed:
  • Paul S. Koh

Abstract

Empirically, many strategic settings are characterized by stable outcomes in which players' decisions are publicly observed, yet no player takes the opportunity to deviate. To analyze such situations in the presence of incomplete information, we build an empirical framework by introducing a novel solution concept that we call Bayes stable equilibrium. Our framework allows the researcher to be agnostic about players' information and the equilibrium selection rule. The Bayes stable equilibrium identified set collapses to the complete information pure strategy Nash equilibrium identified set under strong assumptions on players' information. Furthermore, all else equal, it is weakly tighter than the Bayes correlated equilibrium identified set. We also propose computationally tractable approaches for estimation and inference. In an application, we study the strategic entry decisions of McDonald's and Burger King in the US. Our results highlight the identifying power of informational assumptions and show that the Bayes stable equilibrium identified set can be substantially tighter than the Bayes correlated equilibrium identified set. In a counterfactual experiment, we examine the impact of increasing access to healthy food on the market structures in Mississippi food deserts.

Suggested Citation

  • Paul S. Koh, 2022. "Stable Outcomes and Information in Games: An Empirical Framework," Papers 2205.04990, arXiv.org.
  • Handle: RePEc:arx:papers:2205.04990
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2205.04990
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    2. Ting Zhu & Vishal Singh, 2009. "Spatial competition with endogenous location choices: An application to discount retailing," Quantitative Marketing and Economics (QME), Springer, vol. 7(1), pages 1-35, March.
    3. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    4. Green, Jerry R & Laffont, Jean-Jacques, 1987. "Posterior Implementability in a Two-Person Decision Problem," Econometrica, Econometric Society, vol. 55(1), pages 69-94, January.
    5. Che‐Lin Su & Kenneth L. Judd, 2012. "Constrained Optimization Approaches to Estimation of Structural Models," Econometrica, Econometric Society, vol. 80(5), pages 2213-2230, September.
    6. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    7. Liran Einav, 2010. "Not All Rivals Look Alike: Estimating An Equilibrium Model Of The Release Date Timing Game," Economic Inquiry, Western Economic Association International, vol. 48(2), pages 369-390, April.
    8. Radner, Roy, 1979. "Rational Expectations Equilibrium: Generic Existence and the Information Revealed by Prices," Econometrica, Econometric Society, vol. 47(3), pages 655-678, May.
    9. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    10. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    11. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    13. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
    14. Naoki Aizawa & Hanming Fang, 2020. "Equilibrium Labor Market Search and Health Insurance Reform," Journal of Political Economy, University of Chicago Press, vol. 128(11), pages 4258-4336.
    15. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    16. Mitsuru Igami & Nathan Yang, 2016. "Unobserved heterogeneity in dynamic games: Cannibalization and preemptive entry of hamburger chains in Canada," Quantitative Economics, Econometric Society, vol. 7(2), pages 483-521, July.
    17. Áureo de Paula, 2013. "Econometric Analysis of Games with Multiple Equilibria," Annual Review of Economics, Annual Reviews, vol. 5(1), pages 107-131, May.
    18. Philip G. Gayle & Zijun Luo, 2015. "Choosing between Order-of-Entry Assumptions in Empirical Entry Models: Evidence from Competition between Burger King and McDonald's Restaurant Outlets," Journal of Industrial Economics, Wiley Blackwell, vol. 63(1), pages 129-151, March.
    19. 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.
    20. Hunt Allcott & Rebecca Diamond & Jean-Pierre Dubé & Jessie Handbury & Ilya Rahkovsky & Molly Schnell, 2019. "Food Deserts and the Causes of Nutritional Inequality," The Quarterly Journal of Economics, Oxford University Press, vol. 134(4), pages 1793-1844.
    21. Raphael Thomadsen, 2007. "Product Positioning and Competition: The Role of Location in the Fast Food Industry," Marketing Science, INFORMS, vol. 26(6), pages 792-804, 11-12.
    22. Gualdani, Cristina & Sinha, Shruti, 2019. "Identification and inference in discrete choice models with imperfect information," TSE Working Papers 19-1049, Toulouse School of Economics (TSE), revised Jun 2020.
    23. David B. Ridley, 2008. "Herding versus Hotelling: Market Entry with Costly Information," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 17(3), pages 607-631, September.
    24. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    25. Alfred Galichon & Marc Henry, 2011. "Set Identification in Models with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 78(4), pages 1264-1298.
    26. Cristina Gualdani & Shruti Sinha, 2019. "Identification in discrete choice models with imperfect information," Papers 1911.04529, arXiv.org, revised Jan 2023.
    27. Qingmin Liu, 2020. "Stability and Bayesian Consistency in Two-Sided Markets," American Economic Review, American Economic Association, vol. 110(8), pages 2625-2666, August.
    28. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    29. repec:hrv:faseco:30780157 is not listed on IDEAS
    30. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
    31. Sang Yoon (Tim) Lee & Ananth Seshadri, 2019. "On the Intergenerational Transmission of Economic Status," Journal of Political Economy, University of Chicago Press, vol. 127(2), pages 855-921.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Paul S. Koh, 2022. "Estimating Discrete Games of Complete Information: Bringing Logit Back in the Game," Papers 2205.05002, arXiv.org, revised Jun 2022.
    2. Paul S. Koh, 2022. "Estimating Dynamic Games with Unknown Information Structure," Papers 2205.03706, arXiv.org, revised May 2022.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2022. "Counterfactuals with Latent Information," American Economic Review, American Economic Association, vol. 112(1), pages 343-368, January.
    2. Juan Passadore & Juan Xandri, 2019. "Robust Predictions in Dynamic Policy Games," 2019 Meeting Papers 1345, Society for Economic Dynamics.
    3. Paul S. Koh, 2022. "Estimating Dynamic Games with Unknown Information Structure," Papers 2205.03706, arXiv.org, revised May 2022.
    4. Lin, Zhongjian & Vella, Francis, 2021. "Selection and Endogenous Treatment Models with Social Interactions: An Application to the Impact of Exercise on Self-Esteem," IZA Discussion Papers 14167, Institute of Labor Economics (IZA).
    5. Victor Aguirregabiria, 2021. "Identification of firms’ beliefs in structural models of market competition," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 54(1), pages 5-33, February.
    6. Jos'-Antonio Esp'n-S'nchez & 'lvaro Parra, 2018. "Entry Games under Private Information," Cowles Foundation Discussion Papers 2126, Cowles Foundation for Research in Economics, Yale University.
    7. Ashesh Rambachan, 2022. "Identifying Prediction Mistakes in Observational Data," NBER Chapters, in: Economics of Artificial Intelligence, National Bureau of Economic Research, Inc.
    8. Bergemann, Dirk & Ottaviani, Marco, 2021. "Information Markets and Nonmarkets," CEPR Discussion Papers 16459, C.E.P.R. Discussion Papers.
    9. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Aradillas-López, Andrés & Rosen, Adam M., 2022. "Inference in ordered response games with complete information," Journal of Econometrics, Elsevier, vol. 226(2), pages 451-476.
    11. Bontemps, Christian & Kumar, Rohit, 2020. "A geometric approach to inference in set-identified entry games," Journal of Econometrics, Elsevier, vol. 218(2), pages 373-389.
    12. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2018. "Testing For A General Class Of Functional Inequalities," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1018-1064, October.
    13. Larry G. Epstein & Hiroaki Kaido & Kyoungwon Seo, 2015. "Robust confidence regions for incomplete models," CeMMAP working papers 65/15, Institute for Fiscal Studies.
    14. Pavan, Alessandro & Vives, Xavier, 2015. "Information, Coordination, and Market Frictions: An Introduction," Journal of Economic Theory, Elsevier, vol. 158(PB), pages 407-426.
    15. Cristina Gualdani & Shruti Sinha, 2019. "Identification in discrete choice models with imperfect information," Papers 1911.04529, arXiv.org, revised Jan 2023.
    16. Larry G. Epstein & Hiroaki Kaido & Kyoungwon Seo, 2016. "Robust Confidence Regions for Incomplete Models," Econometrica, Econometric Society, vol. 84, pages 1799-1838, September.
    17. Antonio Penta & Peio Zuazo-Garin, 2019. "Rationalizability, observability and common knowledge," Economics Working Papers 1662, Department of Economics and Business, Universitat Pompeu Fabra.
    18. Larry G. Epstein & Hiroaki Kaido & Kyoungwon Seo, 2015. "Robust confidence regions for incomplete models," CeMMAP working papers 20/15, Institute for Fiscal Studies.
    19. Paul S. Koh, 2022. "Estimating Discrete Games of Complete Information: Bringing Logit Back in the Game," Papers 2205.05002, arXiv.org, revised Jun 2022.
    20. Gualdani, Cristina & Sinha, Shruti, 2019. "Identification and inference in discrete choice models with imperfect information," TSE Working Papers 19-1049, Toulouse School of Economics (TSE), revised Jun 2020.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2205.04990. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://arxiv.org/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.