IDEAS home Printed from https://ideas.repec.org/p/upf/upfgen/1087.html
   My bibliography  Save this paper

Minimax regret and strategic uncertainty

Author

Listed:
  • Ludovic Renou
  • Karl Schlag

Abstract

This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider pricesetting environments and show that optimal pricing policy follows a non-degenerate distribution. The induced price dispersion is consistent with experimental and empirical observations (Baye and Morgan (2004)).

Suggested Citation

  • Ludovic Renou & Karl Schlag, 2008. "Minimax regret and strategic uncertainty," Economics Working Papers 1087, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:1087
    as

    Download full text from publisher

    File URL: https://econ-papers.upf.edu/papers/1087.pdf
    File Function: Whole Paper
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Gary Charness & Matthew Rabin, 2002. "Understanding Social Preferences with Simple Tests," The Quarterly Journal of Economics, Oxford University Press, vol. 117(3), pages 817-869.
    2. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    3. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 817-868.
    4. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    5. Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing: The Case of Regret," Economics Working Papers ECO2005/10, European University Institute.
    6. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
    7. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    8. Dirk Bergemann & Stephen Morris, 2012. "Ex Post Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 3, pages 97-152, World Scientific Publishing Co. Pte. Ltd..
    9. Michael R. Baye & John Morgan, 2004. "Price Dispersion in the Lab and on the Internet: Theory and Evidence," RAND Journal of Economics, The RAND Corporation, vol. 35(3), pages 448-466, Autumn.
    10. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    11. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
    12. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    13. Clemens Puppe & Karl Schlag, 2009. "Choice under complete uncertainty when outcome spaces are state dependent," Theory and Decision, Springer, vol. 66(1), pages 1-16, January.
    14. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    15. Ludovic Renou & Ralph C. Bayer, 2008. "Homo Sapiens Sapiens Meets Homo Strategicus at the Laboratory," Discussion Papers in Economics 08/16, Division of Economics, School of Business, University of Leicester, revised Nov 2008.
    16. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    17. Dirk Bergemann & Karl H. Schlag, 2012. "Pricing Without Priors," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 12, pages 405-415, World Scientific Publishing Co. Pte. Ltd..
    18. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    19. Linhart, P. B. & Radner, R., 1989. "Minimax-regret strategies for bargaining over several variables," Journal of Economic Theory, Elsevier, vol. 48(1), pages 152-178, June.
    20. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(2), pages 227-253, October.
    21. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    22. Peter B. Linhart, 2001. "original papers : Bargaining solutions with non-standard objectives," Review of Economic Design, Springer;Society for Economic Design, vol. 6(2), pages 225-239.
    23. Hayashi, Takashi, 2008. "Regret aversion and opportunity dependence," Journal of Economic Theory, Elsevier, vol. 139(1), pages 242-268, March.
    24. Neeman, Zvika, 1996. "Common Beliefs and the Existence of Speculative Trade," Games and Economic Behavior, Elsevier, vol. 16(1), pages 77-96, September.
    25. Mukerji, S., 1995. "A theory of play for games in strategic form when rationality is not common knowledge," Discussion Paper Series In Economics And Econometrics 9519, Economics Division, School of Social Sciences, University of Southampton.
    26. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
    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. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    2. 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.
    3. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    4. Degan, Arianna & Li, Ming, 2015. "Psychologically-based voting with uncertainty," European Journal of Political Economy, Elsevier, vol. 40(PB), pages 242-259.
    5. Yang, Kai Hao, 2021. "Efficient demands in a multi-product monopoly," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. Iverson, Terrence, 2013. "Minimax regret discounting," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 598-608.
    7. Halpern, Joseph Y. & Pass, Rafael, 2012. "Iterated regret minimization: A new solution concept," Games and Economic Behavior, Elsevier, vol. 74(1), pages 184-207.
    8. Kasberger, Bernhard & Woodward, Kyle, 2021. "Bidding in Multi-Unit Auctions under Limited Information," MPRA Paper 111185, University Library of Munich, Germany.
    9. Stauber, Ronald, 2019. "A strategic product for belief functions," Games and Economic Behavior, Elsevier, vol. 116(C), pages 38-64.
    10. Duffy, John & Ralston, Jason, 2020. "Innovate versus imitate: Theory and experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 177(C), pages 727-751.
    11. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    12. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01337293, HAL.
    13. 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.
    14. Gisèle Umbhauer, 2020. "Market exit and minimax regret," Working Papers of BETA 2020-29, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    15. Philippe Bich, 2016. "Prudent Equilibria and Strategic Uncertainty in Discontinuous Games," Working Papers halshs-01337293, HAL.
    16. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
    17. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    18. Mass, Helene, 2018. "Strategies under strategic uncertainty," ZEW Discussion Papers 18-055, ZEW - Leibniz Centre for European Economic Research.
    19. Ronald Stauber, 2019. "A strategic product for belief functions," ANU Working Papers in Economics and Econometrics 2019-668, Australian National University, College of Business and Economics, School of Economics.
    20. Bich, Philippe, 2019. "Strategic uncertainty and equilibrium selection in discontinuous games," Journal of Economic Theory, Elsevier, vol. 183(C), pages 786-822.
    21. Karl Schlag & Andriy Zapechelnyuk, 2020. "Compromise, Don't Optimize: Generalizing Perfect Bayesian Equilibrium to Allow for Ambiguity," Papers 2003.02539, arXiv.org, revised Sep 2021.
    22. Bernhard Kasberger, 2022. "An Equilibrium Model of the First-Price Auction with Strategic Uncertainty: Theory and Empirics," Papers 2202.07517, arXiv.org, revised Mar 2022.
    23. Valerio Capraro & Joseph Y Halpern, 2019. "Translucent players: Explaining cooperative behavior in social dilemmas," Rationality and Society, , vol. 31(4), pages 371-408, November.

    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 & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    2. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November.
    3. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    4. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
    5. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    6. Yi-Chun Chen & Xiao Luo & Chen Qu, 2016. "Rationalizability in general situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 147-167, January.
    7. Bernhard Kasberger, 2022. "An Equilibrium Model of the First-Price Auction with Strategic Uncertainty: Theory and Empirics," Papers 2202.07517, arXiv.org, revised Mar 2022.
    8. Takashi Hayashi, 2011. "Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret," Theory and Decision, Springer, vol. 70(4), pages 399-430, April.
    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.
    10. Vitaly Pruzhansky, 2004. "A Discussion of Maximin," Tinbergen Institute Discussion Papers 04-028/1, Tinbergen Institute.
    11. Segal, Uzi & Sobel, Joel, 2007. "Tit for tat: Foundations of preferences for reciprocity in strategic settings," Journal of Economic Theory, Elsevier, vol. 136(1), pages 197-216, September.
    12. Kin Chung Lo, 1998. "Epistemic Conditions for Agreement and Stochastic Independence of epsilon-Contaminated Beliefs," Working Papers 1998_02, York University, Department of Economics.
    13. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    14. Luo, Xiao & Ma, Chenghu, 2001. "Stable equilibrium in beliefs in extensive games with perfect information," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1801-1825, November.
    15. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    16. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    17. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    18. Thomas Jungbauer & Klaus Ritzberger, 2011. "Strategic games beyond expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 377-398, October.
    19. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(1), pages 1-12, September.
    20. Mass, Helene, 2018. "Strategies under strategic uncertainty," ZEW Discussion Papers 18-055, ZEW - Leibniz Centre for European Economic Research.

    More about this item

    Keywords

    Minimax regret; rationality; conjectures; price dispersion; auction;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

    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:upf:upfgen:1087. 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://www.econ.upf.edu/ .

    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: http://www.econ.upf.edu/ .

    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.