IDEAS home Printed from https://ideas.repec.org/p/pen/papers/21-020.html
   My bibliography  Save this paper

Evolutionarily Stable (Mis)specifications:Theory and Applications

Author

Listed:
  • Kevin He

    (University of Pennsylvania)

  • Jonathan Libgober

    (University of Southern California)

Abstract

We introduce an evolutionary framework to evaluate competing (mis)specifications in strategic situations, focusing on which misspecifications can persist over correct specifications. Agents with heterogeneous specifications coexist in a society and repeatedly play a stage game against random opponents, drawing Bayesian inferences about the environment based on personal experience. One specification is evolutionarily stable against another if, when-ever sufficiently prevalent, its adherents obtain higher average payoffs than their counterparts. Agents’ equilibrium beliefs are constrained but not wholly determined by specifications. En-dogenous belief formation through the learning channel generates novel stability phenomena compared to frameworks where single beliefs are the heritable units of cultural transmission. In linear-quadratic-normal games where players receive correlated signals but possibly misperceive the information structure, the correct specification is evolutionarily unstable against a correlational error whose direction depends on social interaction structure. We also endogenize coarse thinking in games and show how its prevalence varies with game parameters.

Suggested Citation

  • Kevin He & Jonathan Libgober, 2021. "Evolutionarily Stable (Mis)specifications:Theory and Applications," PIER Working Paper Archive 21-020, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Handle: RePEc:pen:papers:21-020
    as

    Download full text from publisher

    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/21-020.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. In-Koo Cho & Kenneth Kasa, 2015. "Learning and Model Validation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(1), pages 45-82.
    2. Dasaratha, Krishna & He, Kevin, 2020. "Network structure and naive sequential learning," Theoretical Economics, Econometric Society, vol. 15(2), May.
    3. Dirk Bergemann & Stephen Morris, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    4. Heller, Yuval, 2015. "Three steps ahead," Theoretical Economics, Econometric Society, vol. 10(1), January.
    5. Nyarko, Yaw, 1991. "Learning in mis-specified models and the possibility of cycles," Journal of Economic Theory, Elsevier, vol. 55(2), pages 416-427, December.
    6. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    7. Joshua Schwartzstein & Adi Sunderam, 2021. "Using Models to Persuade," American Economic Review, American Economic Association, vol. 111(1), pages 276-323, January.
    8. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 997-1026, August.
    9. Ingela Alger & Jörgen W. Weibull, 2019. "Evolutionary Models of Preference Formation," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 329-354, August.
    10. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    11. Ignacio Esponda & Demian Pouzo & Yuichi Yamamoto, 2019. "Asymptotic Behavior of Bayesian Learners with Misspecified Models," Papers 1904.08551, arXiv.org, revised Oct 2019.
    12. George-Marios Angeletos & Alessandro Pavan, 2007. "Efficient Use of Information and Social Value of Information," Econometrica, Econometric Society, vol. 75(4), pages 1103-1142, July.
    13. Pooya Molavi, 2019. "Macroeconomics with Learning and Misspecification: A General Theory and Applications," 2019 Meeting Papers 1584, Society for Economic Dynamics.
    14. Vives, Xavier, 1988. "Aggregation of Information in Large Cournot Markets," Econometrica, Econometric Society, vol. 56(4), pages 851-876, July.
    15. Kfir Eliaz & Ran Spiegler, 2020. "A Model of Competing Narratives," American Economic Review, American Economic Association, vol. 110(12), pages 3786-3816, December.
    16. Eddie Dekel & Jeffrey C. Ely & Okan Yilankaya, 2007. "Evolution of Preferences -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 685-704.
    17. Berman, Ron & Heller, Yuval, 2020. "Naive Analytics Equilibrium," MPRA Paper 103824, University Library of Munich, Germany.
    18. Fudenberg, Drew & Romanyuk, Gleb & Strack, Philipp, 2017. "Active learning with a misspecified prior," Theoretical Economics, Econometric Society, vol. 12(3), September.
    19. Bohren, J. Aislinn, 2016. "Informational herding with model misspecification," Journal of Economic Theory, Elsevier, vol. 163(C), pages 222-247.
    20. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Stability and Robustness in Misspecified Learning Models," Cowles Foundation Discussion Papers 2235, Cowles Foundation for Research in Economics, Yale University.
    21. He, Kevin, 2022. "Mislearning from censored data: The gambler's fallacy and other correlational mistakes in optimal-stopping problems," Theoretical Economics, Econometric Society, vol. 17(3), July.
    22. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, April.
    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. Jehiel, Philippe & Mohlin, Erik, 2021. "Cycling and Categorical Learning in Decentralized Adverse Selection Economies," Working Papers 2021:11, Lund University, Department of Economics.
    2. Cuimin Ba, 2021. "Robust Misspecified Models and Paradigm Shifts," Papers 2106.12727, arXiv.org, revised Aug 2023.
    3. Drew Fudenberg & Giacomo Lanzani & Philipp Strack, 2021. "Limit Points of Endogenous Misspecified Learning," Econometrica, Econometric Society, vol. 89(3), pages 1065-1098, May.
    4. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Welfare Comparisons for Biased Learning," Cowles Foundation Discussion Papers 2274R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2021.

    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. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Misinterpreting Others and the Fragility of Social Learning," Econometrica, Econometric Society, vol. 88(6), pages 2281-2328, November.
    2. Ignacio Esponda & Demian Pouzo & Yuichi Yamamoto, 2019. "Asymptotic Behavior of Bayesian Learners with Misspecified Models," Papers 1904.08551, arXiv.org, revised Oct 2019.
    3. Cuimin Ba, 2021. "Robust Misspecified Models and Paradigm Shifts," Papers 2106.12727, arXiv.org, revised Aug 2023.
    4. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Stability and Robustness in Misspecified Learning Models," Cowles Foundation Discussion Papers 2235, Cowles Foundation for Research in Economics, Yale University.
    5. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Belief Convergence under Misspecified Learning: A Martingale Approach," Cowles Foundation Discussion Papers 2235R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2021.
    6. Mira Frick & Ryota Iijima & Yuhta Ishii, 2020. "Belief Convergence under Misspecified Learning: A Martingale Approach," Cowles Foundation Discussion Papers 2235R3, Cowles Foundation for Research in Economics, Yale University, revised Apr 2022.
    7. Yingkai Li & Harry Pei, 2020. "Misspecified Beliefs about Time Lags," Papers 2012.07238, arXiv.org.
    8. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Welfare Comparisons for Biased Learning," Cowles Foundation Discussion Papers 2274, Cowles Foundation for Research in Economics, Yale University.
    9. Mira Frick & Ryota Iijima & Yuhta Ishii, 2018. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2128R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2019.
    10. José Luis Montiel Olea & Pietro Ortoleva & Mallesh Pai & Andrea Prat, 2021. "Competing Models," Working Papers 2021-89, Princeton University. Economics Department..
    11. J. Aislinn Bohren & Daniel N. Hauser, 2023. "Behavioral Foundations of Model Misspecification," PIER Working Paper Archive 23-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    12. Fudenberg, Drew & Lanzani, Giacomo & Strack, Philipp, 2023. "Pathwise concentration bounds for Bayesian beliefs," Theoretical Economics, Econometric Society, vol. 18(4), November.
    13. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    14. Bowen, T. Renee & Galperti, Simone & Dmitriev, Danil, 2021. "Learning from Shared News: When Abundant Information Leads to Belief Polarization," CEPR Discussion Papers 15789, C.E.P.R. Discussion Papers.
    15. Gagnon-Bartsch, Tristan & Bushong, Benjamin, 2022. "Learning with misattribution of reference dependence," Journal of Economic Theory, Elsevier, vol. 203(C).
    16. Takeshi Murooka & Yuichi Yamamoto, 2021. "Misspecified Bayesian Learning by Strategic Players: First-Order Misspecification and Higher-Order Misspecification," OSIPP Discussion Paper 21E008, Osaka School of International Public Policy, Osaka University.
    17. Philippe Jehiel & Erik Mohlin, 2023. "Categorization in Games: A Bias-Variance Perspective," Working Papers halshs-04154272, HAL.
    18. Takeshi Murooka & Yuichi Yamamoto, 2021. "Multi-Player Bayesian Learning with Misspecified Models," OSIPP Discussion Paper 21E001, Osaka School of International Public Policy, Osaka University.
    19. Esponda, Ignacio & Pouzo, Demian & Yamamoto, Yuichi, 2021. "Asymptotic behavior of Bayesian learners with misspecified models," Journal of Economic Theory, Elsevier, vol. 195(C).
    20. Ba, Cuimin & Gindin, Alice, 2023. "A multi-agent model of misspecified learning with overconfidence," Games and Economic Behavior, Elsevier, vol. 142(C), pages 315-338.

    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:pen:papers:21-020. See general information about how to correct material in RePEc.

    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: Administrator (email available below). General contact details of provider: https://edirc.repec.org/data/deupaus.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.