IDEAS home Printed from https://ideas.repec.org/p/bai/series/economia-series12.html
   My bibliography  Save this paper

Monty Hall's Three Doors for Dummies

Author

Listed:
  • Andrea Morone

    (University of Bari - Department of Economics and Mathematical Methods)

  • Annamaria Fiore

    (University of Bari - Department of Economics and Mathematical Methods)

Abstract

Monty Hall's three doors problem is a well-known "anomaly" in economics. It appears to be an example of a systematic violation of the assumption of subjects' rationality. Many papers have studied the Monty Hall anomaly under different perspectives (i.e. computerizing, learning, grouping, talking, and even teaching how to play it), but the anomaly still survives. The most common explanation for this is that subjects are unable to carry out correctly the Bayesian updating necessary. Our approach is different from all previous attempts to explain and correct the Monty Hall anomaly, inasmuch we developed a more radical "debiasing test". Even if the game remains identical in terms of probabilities and subjects task, we eliminate the necessity for any Bayesian updating, as our new framework does not require subjects to make any probability calculations. Consequently, having eliminated the cause, also the effect should have disappeared. In order to make our results robust, we also run an intermediate treatment. Even though we observe an evident monotonic increase in the switching percentage across the three treatments, as we expected (from 41.5% in the treatment that replicates the standard design, to 45.5% for the intermediate treatment, up to 58% in the new framework), this percentage remains still too low, even though no Bayesian updating is involved. These results drive us to conclude that this anomaly, even if attenuated by design conditions, is not a weak effect, but rather a systematic behavioural regularity. It could be attributed to some psychological underpinnings, such as the status quo bias. We comment on these, and alternative explanations, in our conclusions.

Suggested Citation

  • Andrea Morone & Annamaria Fiore, 2007. "Monty Hall's Three Doors for Dummies," SERIES 0012, Dipartimento di Economia e Finanza - Università degli Studi di Bari "Aldo Moro", revised Feb 2007.
  • Handle: RePEc:bai:series:economia-series12
    as

    Download full text from publisher

    File URL: http://www.seriesworkingpapers.it/RePEc/bai/series/Economia-Series12.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    2. Friedman, Daniel, 1998. "Monty Hall's Three Doors: Construction and Deconstruction of a Choice Anomaly," American Economic Review, American Economic Association, vol. 88(4), pages 933-946, September.
    3. Slembeck, Tilman & Tyran, Jean-Robert, 2004. "Do institutions promote rationality?: An experimental study of the three-door anomaly," Journal of Economic Behavior & Organization, Elsevier, vol. 54(3), pages 337-350, July.
    4. Daniel Kahneman & Jack L. Knetsch & Richard H. Thaler, 1991. "Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias," Journal of Economic Perspectives, American Economic Association, vol. 5(1), pages 193-206, Winter.
    5. Page, Scott E., 1998. "Let's make a deal," Economics Letters, Elsevier, vol. 61(2), pages 175-180, November.
    6. Ignacio Palacios-Huerta, 2003. "Learning to Open Monty Hall's Doors," Experimental Economics, Springer;Economic Science Association, vol. 6(3), pages 235-251, November.
    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. Andrea Morone & Rocco Caferra & Alessia Casamassima & Alessandro Cascavilla & Paola Tiranzoni, 2021. "Three doors anomaly, “should I stay, or should I go”: an artefactual field experiment," Theory and Decision, Springer, vol. 91(3), pages 357-376, October.

    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. Brain Kluger & Daniel Friedman, 2006. "Financial Engineering and Rationality: Experimental Evidence Based on the Monty Hall Problem," Labsi Experimental Economics Laboratory University of Siena 007, University of Siena.
    2. Slembeck, Tilman & Tyran, Jean-Robert, 2004. "Do institutions promote rationality?: An experimental study of the three-door anomaly," Journal of Economic Behavior & Organization, Elsevier, vol. 54(3), pages 337-350, July.
    3. Andrea Morone & Rocco Caferra & Alessia Casamassima & Alessandro Cascavilla & Paola Tiranzoni, 2021. "Three doors anomaly, “should I stay, or should I go”: an artefactual field experiment," Theory and Decision, Springer, vol. 91(3), pages 357-376, October.
    4. Kim Kaivanto & Eike B. Kroll & Michael Zabinski, 2014. "Bias-Trigger Manipulation and Task-Form Understanding in Monty Hall," Economics Bulletin, AccessEcon, vol. 34(1), pages 89-98.
    5. Philipp E. Otto, 2022. "Monty Hall three door ’anomaly’ revisited: a note on deferment in an extensive form game," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 21(1), pages 25-35, June.
    6. Engelmann, Dirk & Strobel, Martin, 2012. "Deconstruction and reconstruction of an anomaly," Games and Economic Behavior, Elsevier, vol. 76(2), pages 678-689.
    7. Sebastian Fehrler & Baiba Renerte & Irenaeus Wolff, 2020. "Beliefs about Others: A Striking Example of Information Neglect," TWI Research Paper Series 118, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    8. Tilman Slembeck, 2000. "Learning in Economics: Where Do We Stand?," Microeconomics 0004007, University Library of Munich, Germany.
    9. Tian, Ye & Chiu, Yi-Chang & Sun, Jian, 2019. "Understanding behavioral effects of tradable mobility credit scheme: An experimental economics approach," Transport Policy, Elsevier, vol. 81(C), pages 1-11.
    10. Patt, Anthony G. & Bowles, Hannah Riley & Cash, David W., 2006. "Mechanisms for Enhancing the Credibility of an Adviser: Prepayment and Aligned Incentives," Working Paper Series rwp06-010, Harvard University, John F. Kennedy School of Government.
    11. Ignacio Palacios-Huerta, 2003. "Learning to Open Monty Hall's Doors," Experimental Economics, Springer;Economic Science Association, vol. 6(3), pages 235-251, November.
    12. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    13. Elmaghraby, Wedad J. & Larson, Nathan, 2012. "Explaining deviations from equilibrium in auctions with avoidable fixed costs," Games and Economic Behavior, Elsevier, vol. 76(1), pages 131-159.
    14. Vincent P. Crawford & Nagore Iriberri, 2007. "Level-k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?," Econometrica, Econometric Society, vol. 75(6), pages 1721-1770, November.
    15. Francisco Gomes & Michael Haliassos & Tarun Ramadorai, 2021. "Household Finance," Journal of Economic Literature, American Economic Association, vol. 59(3), pages 919-1000, September.
    16. Dan Levin & James Peck & Asen Ivanov, 2016. "Separating Bayesian Updating from Non-Probabilistic Reasoning: An Experimental Investigation," American Economic Journal: Microeconomics, American Economic Association, vol. 8(2), pages 39-60, May.
    17. Dirk Engelmann & Martin Strobel, 2004. "The False Consensus Effect: Deconstruction and Reconstruction of an Anomaly," CERGE-EI Working Papers wp233, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    18. Lunawat, Radhika, 2021. "Learning from trading activity in laboratory security markets with higher-order uncertainty," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 90(C).
    19. David V. Budescu & Boris Maciejovsky, 2005. "The Effect of Payoff Feedback and Information Pooling on Reasoning Errors: Evidence from Experimental Markets," Management Science, INFORMS, vol. 51(12), pages 1829-1843, December.
    20. David V. Budescu & Boris Maciejovsky, "undated". "Reasoning and Institutions: Do Markets Facilitate Logical Reasoning in the Wason Selection Task?," Papers on Strategic Interaction 2003-04, Max Planck Institute of Economics, Strategic Interaction Group.

    More about this item

    Keywords

    Learning; Anomaly; Individual decision making;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior

    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:bai:series:economia-series12. 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: Annalisa Vinella (email available below). General contact details of provider: https://edirc.repec.org/data/debarit.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.