IDEAS home Printed from https://ideas.repec.org/p/ulp/sbbeta/2021-48.html
   My bibliography  Save this paper

Minimax regret in the 11-20 money request game

Author

Listed:
  • Gisèle Umbhauer

Abstract

Arad and Rubinstein’s 11-20 money request game nicely triggers level-k reasoning. Yet we show that mixed-strategy minimax regret, in a general class of money-request games, mimics a level-k reasoning, at least if the number of players is supposed to decrease in the depth of reasoning. We also show that, in this class of games, the minimax regret probability distribution is the exact reverse of the mixed-strategy Nash equilibrium distribution, and that minimax regret leads to a larger expected payoff than the Nash equilibrium payoff.

Suggested Citation

  • Gisèle Umbhauer, 2021. "Minimax regret in the 11-20 money request game," Working Papers of BETA 2021-48, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  • Handle: RePEc:ulp:sbbeta:2021-48
    as

    Download full text from publisher

    File URL: http://beta.u-strasbg.fr/WP/2021/2021-48.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    2. Eduardo Fé & David Gill & Victoria Prowse, 2022. "Cognitive Skills, Strategic Sophistication, and Life Outcomes," Journal of Political Economy, University of Chicago Press, vol. 130(10), pages 2643-2704.
    3. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    4. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2013. "Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications," Journal of Economic Literature, American Economic Association, vol. 51(1), pages 5-62, March.
    5. King King Li & Kang Rong, 2018. "Choices in the 11–20 Game: The Role of Risk Aversion," Games, MDPI, vol. 9(3), pages 1-14, July.
    6. García-Pola, Bernardo, 2020. "Do people minimize regret in strategic situations? A level-k comparison," Games and Economic Behavior, Elsevier, vol. 124(C), pages 82-104.
    7. Gisèle Umbhauer, 2020. "Market exit and minimax regret," Working Papers of BETA 2020-29, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    8. Ayala Arad & Ariel Rubinstein, 2012. "The 11-20 Money Request Game: A Level-k Reasoning Study," American Economic Review, American Economic Association, vol. 102(7), pages 3561-3573, December.
    9. Halpern, Joseph Y. & Pass, Rafael, 2012. "Iterated regret minimization: A new solution concept," Games and Economic Behavior, Elsevier, vol. 74(1), pages 184-207.
    Full references (including those not matched with items on IDEAS)

    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. García-Pola, Bernardo, 2020. "Do people minimize regret in strategic situations? A level-k comparison," Games and Economic Behavior, Elsevier, vol. 124(C), pages 82-104.
    2. Alaoui, Larbi & Janezic, Katharina A. & Penta, Antonio, 2020. "Reasoning about others' reasoning," Journal of Economic Theory, Elsevier, vol. 189(C).
    3. Choo, Lawrence C.Y & Kaplan, Todd R., 2014. "Explaining Behavior in the "11-20" Game," MPRA Paper 52808, University Library of Munich, Germany.
    4. Llorente-Saguer, Aniol & Sheremeta, Roman & Szech, Nora, 2016. "Designing Contests Between Heterogeneous Contestants: An Experimental Study of Tie-Breaks and Bid-Caps in All-Pay Auctions," MPRA Paper 71202, University Library of Munich, Germany.
    5. Nagel, Rosemarie & Bühren, Christoph & Frank, Björn, 2017. "Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 191-207.
    6. Mariana García-Schmidt & Michael Woodford, 2019. "Are Low Interest Rates Deflationary? A Paradox of Perfect-Foresight Analysis," American Economic Review, American Economic Association, vol. 109(1), pages 86-120, January.
    7. Itzhak Rasooly, 2022. "Going...going...wrong: a test of the level-k (and cognitive hierarchy) models of bidding behaviour," Economics Series Working Papers 959, University of Oxford, Department of Economics.
    8. Berger, Ulrich & De Silva, Hannelore & Fellner-Röhling, Gerlinde, 2016. "Cognitive hierarchies in the minimizer game," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 337-348.
    9. Carlos Alós-Ferrer & Johannes Buckenmaier, 2021. "Cognitive sophistication and deliberation times," Experimental Economics, Springer;Economic Science Association, vol. 24(2), pages 558-592, June.
    10. Itzhak Rasooly, 2021. "Going... going... wrong: a test of the level-k (and cognitive hierarchy) models of bidding behaviour," Papers 2111.05686, arXiv.org.
    11. Kota Murayama, 2015. "Robust Predictions under Finite Depth of Reasoning," Discussion Paper Series DP2015-28, Research Institute for Economics & Business Administration, Kobe University.
    12. Marcus Dittrich & Kristina Leipold, 2014. "Gender Differences in Strategic Reasoning," CESifo Working Paper Series 4763, CESifo.
    13. Lindner, Florian & Sutter, Matthias, 2013. "Level-k reasoning and time pressure in the 11–20 money request game," Economics Letters, Elsevier, vol. 120(3), pages 542-545.
    14. Allred, Sarah & Duffy, Sean & Smith, John, 2016. "Cognitive load and strategic sophistication," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 162-178.
    15. María Cubel & Santiago Sanchez-Pages, 2014. "Gender differences and stereotypes in the beauty contest," Working Papers 2014/13, Institut d'Economia de Barcelona (IEB).
    16. Irenaeus Wolff, 2017. "Lucky Numbers in Simple Games," TWI Research Paper Series 107, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    17. María Cubel & Santiago Sanchez-Pages, 2014. "Gender differences and stereotypes in the beauty contest," Working Papers 2014/13, Institut d'Economia de Barcelona (IEB).
    18. Li, Ying Xue & Schipper, Burkhard C., 2020. "Strategic reasoning in persuasion games: An experiment," Games and Economic Behavior, Elsevier, vol. 121(C), pages 329-367.
    19. Georganas, Sotiris & Healy, Paul J. & Weber, Roberto A., 2015. "On the persistence of strategic sophistication," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 369-400.
    20. Maria Cubel & Santiago Sanchez-Pages, 2016. "Gender differences and stereotypes in strategic thinking," UB Economics Working Papers 2016/338, Universitat de Barcelona, Facultat d'Economia i Empresa, UB School of Economics.

    More about this item

    Keywords

    minimax regret; level-k reasoning; money-request game; Nash equilibrium.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:ulp:sbbeta:2021-48. 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: https://edirc.repec.org/data/bestrfr.html .

    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: The email address of this maintainer does not seem to be valid anymore. Please ask the person in charge to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/bestrfr.html .

    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.