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Choquet Rationality

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  • Ghirardato, Paolo
  • Le Breton, Michel

Abstract

We provide a characterization of the consequences of the assumption that a decision maker with a given utility function is Choquet rational: She maximizes expected utility, but possibly with respect to non-additive beliefs, so that her preferences are represented by Choquet expected utility (CEU). The characterization shows that this notion of rationality allows in generalto rationalize more choices than it is possible when beliefs have to be additive. More surprisingly, we find that a considerable restriction on the types of beliefs allowed does not change the set of rational actions. We then remark on the relation between the predictions of CEU model, of a similar model (the maxmin expected utility model), and those of subjective expected utility when the risk attitude of the decision maker is not known. We close with an application of the result to the definition of a solution concept (in the spirit of rationalizability) for strategic-form games.

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Bibliographic Info

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

Volume (Year): 90 (2000)
Issue (Month): 2 (February)
Pages: 277-285

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Handle: RePEc:eee:jetheo:v:90:y:2000:i:2:p:277-285

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

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References

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  1. Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February.
  2. Eichberger, Jurgen & Kelsey, David, 1996. "Uncertainty Aversion and Preference for Randomisation," Journal of Economic Theory, Elsevier, vol. 71(1), pages 31-43, October.
  3. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  4. Ebbe Hendon & Hans Jorgen Jacobsen & Birgitte Sloth & Torben Tranaes, 1995. "NASH Equilibrium in Lower Probabilities," Discussion Papers 95-09, University of Copenhagen. Department of Economics.
  5. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401.
  6. Epstein, Larry G & Wang, Tan, 1996. ""Beliefs about Beliefs" without Probabilities," Econometrica, Econometric Society, vol. 64(6), pages 1343-73, November.
  7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  8. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
  9. Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December.
  10. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  11. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  12. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  13. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  14. Border, Kim C., 1992. "Revealed preference, stochastic dominance, and the expected utility hypothesis," Journal of Economic Theory, Elsevier, vol. 56(1), pages 20-42, February.
  15. Peter Kilbanoff, 1996. "Characterizing Uncertainty Aversion Through Preference for Mixtures," Discussion Papers 1159, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  16. Epstein, Larry G., 1997. "Preference, Rationalizability and Equilibrium," Journal of Economic Theory, Elsevier, vol. 73(1), pages 1-29, March.
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Citations

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Cited by:
  1. 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.
  2. Alexander Zimper, 2007. "Strategic games with security and potential level players," Theory and Decision, Springer, vol. 63(1), pages 53-78, August.
  3. Zimper, Alexander, 2006. "Uniqueness conditions for strongly point-rationalizable solutions to games with metrizable strategy sets," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 729-751, September.
  4. Zimper, Alexander, 2005. "Equivalence between best responses and undominated," Sonderforschungsbereich 504 Publications 05-08, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  5. Silvia Bortot & Mario Fedrizzi & Silvio Giove, 2011. "Modelling fraud detection by attack trees and Choquet integral," DISA Working Papers 2011/09, Department of Computer and Management Sciences, University of Trento, Italy, revised 31 Aug 2011.
  6. Roman Kozhan, 2011. "Non-additive anonymous games," International Journal of Game Theory, Springer, vol. 40(2), pages 215-230, May.
  7. Lo, Kin Chung, 2007. "Sharing beliefs about actions," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 123-133, March.
  8. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
  9. Yi-Chun Chen & Xiao Luo, 2012. "An indistinguishability result on rationalizability under general preferences," Economic Theory, Springer, vol. 51(1), pages 1-12, September.
  10. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November.
  11. repec:ebl:ecbull:v:3:y:2005:i:7:p:1-6 is not listed on IDEAS
  12. Lo, Kin Chung, 2006. "Agreement and stochastic independence of belief functions," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 1-22, January.
  13. Alexander Zimper, 2005. "Equivalence between best responses and undominated strategies: a generalization from finite to compact strategy sets," Economics Bulletin, AccessEcon, vol. 3(7), pages 1-6.
  14. Luo, Xiao & Ma, Chenghu, 2003. ""Agreeing to disagree" type results: a decision-theoretic approach," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 849-861, November.
  15. Denneberg, Dieter, 2002. "Conditional expectation for monotone measures, the discrete case," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 105-121, April.

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