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Axioms for minimax regret choice correspondences

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Author Info

  • Stoye, Jörg

Abstract

This paper unifies and extends the recent axiomatic literature on minimax regret. It compares several models of minimax regret, shows how to characterize the according choice correspondences in a unified setting, extends one of them to choice from convex (through randomization) sets, and connects them by defining a behavioral notion of perceived ambiguity. Substantively, a main idea is to behaviorally identify ambiguity with failures of independence of irrelevant alternatives. Regarding proof technique, the core contribution is to uncover a dualism between choice correspondences and preferences in an environment where this dualism is not obvious. This insight can be used to generate results by importing findings from the existing literature on preference orderings.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 146 (2011)
Issue (Month): 6 ()
Pages: 2226-2251

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Handle: RePEc:eee:jetheo:v:146:y:2011:i:6:p:2226-2251

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Minimax regret; Ambiguity; Ambiguity aversion; Multiple priors; Choice correspondences;

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References

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  1. Cohen, Michele & Jaffray, Jean-Yves, 1980. "Rational Behavior under Complete Ignorance," Econometrica, Econometric Society, vol. 48(5), pages 1281-99, July.
  2. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2005. "Certainty Independence and the Separation of Utility and Beliefs," Journal of Economic Theory, Elsevier, vol. 120(1), pages 129-136, January.
  3. Dirk Bergemann & Karl H. Schlag, 2007. "Pricing without Priors," Cowles Foundation Discussion Papers 1625, Cowles Foundation for Research in Economics, Yale University.
  4. Charles F. Manski, 2004. "Statistical Treatment Rules for Heterogeneous Populations," Econometrica, Econometric Society, vol. 72(4), pages 1221-1246, 07.
  5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  6. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-92, July.
  7. Stoye, J rg, 2007. "Minimax Regret Treatment Choice With Incomplete Data And Many Treatments," Econometric Theory, Cambridge University Press, vol. 23(01), pages 190-199, February.
  8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  9. Sugden Robert, 1993. "An Axiomatic Foundation for Regret Theory," Journal of Economic Theory, Elsevier, vol. 60(1), pages 159-180, June.
  10. Ludovic Renou & Karl H. Schlag, 2009. "Implementation in Minimax Regret Equilibrium," Discussion Papers in Economics 09/24, Department of Economics, University of Leicester.
  11. Chamberlain, Gary, 2000. "Econometrics and decision theory," Journal of Econometrics, Elsevier, vol. 95(2), pages 255-283, April.
  12. Loomes, Graham & Sugden, Robert, 1982. "Regret Theory: An Alternative Theory of Rational Choice under Uncertainty," Economic Journal, Royal Economic Society, vol. 92(368), pages 805-24, December.
  13. Ortoleva, Pietro, 2008. "Status Quo Bias, Multiple Priors and Uncertainty Aversion," MPRA Paper 12243, University Library of Munich, Germany.
  14. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
  15. repec:hal:cesptp:halshs-00442869 is not listed on IDEAS
  16. Raphaël Giraud & Jean-Marc Tallon, 2009. "Are beliefs a matter of taste ? A case for objective imprecise information," Documents de travail du Centre d'Economie de la Sorbonne 09086, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  17. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
  18. Hansen, Bruce E., 2005. "Exact Mean Integrated Squared Error Of Higher Order Kernel Estimators," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1031-1057, December.
  19. Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
  20. Jürg Niehans, 1948. "Zur Preisbildungen bei ungewissen Erwartungen," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 84(V), pages 433-456.
  21. 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.
  22. W. Pesendorfer & F. Gul, 1999. "Temptation and Self-Control," Princeton Economic Theory Papers 99f1, Economics Department, Princeton University.
  23. Droge, Bernd, 2006. "Minimax regret comparison of hard and soft thresholding for estimating a bounded normal mean," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 83-92, January.
  24. Ludovic Renou & Karl H. Schlag, 2008. "Minimax regret and strategic uncertainty," Discussion Papers in Economics 08/2, Department of Economics, University of Leicester, revised Apr 2008.
  25. 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.
  26. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003.
  27. Zen Mei-Mei & DasGupta A., 1993. "Estimating A Binomial Parameter: Is Robust Bayes Real Bayes?," Statistics & Risk Modeling, De Gruyter, vol. 11(1), pages 37-60, January.
  28. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  29. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, 09.
  30. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  31. Manski, Charles F., 2007. "Minimax-regret treatment choice with missing outcome data," Journal of Econometrics, Elsevier, vol. 139(1), pages 105-115, July.
  32. Todd Sarver, 2008. "Anticipating Regret: Why Fewer Options May Be Better," Econometrica, Econometric Society, vol. 76(2), pages 263-305, 03.
  33. Hayashi, Takashi, 2009. "Stopping with anticipated regret," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 479-490, July.
  34. Fishburn, Peter C., 1989. "Non-transitive measurable utility for decision under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 187-207, April.
  35. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  36. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
  37. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
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Citations

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Cited by:
  1. Dirk Bergemann & Karl Schlag, 2007. "Robust Monopoly Pricing," Levine's Bibliography 321307000000000983, UCLA Department of Economics.
  2. Dirk Bergemann & Karl H. Schlag, 2007. "Pricing without Priors," Cowles Foundation Discussion Papers 1625, Cowles Foundation for Research in Economics, Yale University.
  3. Joseph Y. Halpern & Samantha Leung, 2012. "Weighted Sets of Probabilities and MinimaxWeighted Expected Regret: New Approaches for Representing Uncertainty and Making Decisions," Papers 1210.4853, arXiv.org.
  4. Takashi Hayashi, 2008. "Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret," KIER Working Papers 659, Kyoto University, Institute of Economic Research.
  5. Stoye, Jörg, 2009. "Minimax regret treatment choice with finite samples," Journal of Econometrics, Elsevier, vol. 151(1), pages 70-81, July.
  6. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
  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. 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. Zhe Yang & Yong Pu, 2012. "Existence and stability of minimax regret equilibria," Journal of Global Optimization, Springer, vol. 54(1), pages 17-26, September.
  10. Eddie Dekel & Barton L. Lipman, 2009. "How (Not) to Do Decision Theory," Levine's Working Paper Archive 814577000000000339, David K. Levine.
  11. John D Hey & Gianna Lotito & Anna Maffioletti, 2008. "The Descriptive and Predictive Adequacy of Theories of Decision Making Under Uncertainty/Ambiguity," Discussion Papers 08/04, Department of Economics, University of York.
  12. Hayashi, Takashi, 2009. "Stopping with anticipated regret," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 479-490, July.

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