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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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Suggested Citation

  • GHIRARDATO, Paolo & LE BRETON, Michel, 2000. "Choquet rationality," LIDAM Reprints CORE 1447, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:1447
    DOI: 10.1006/jeth.1999.2599
    Note: In : Journal of Economic Theory, 90, 277-285, 2000
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    2. Lo, Kin Chung, 2002. "Correlated equilibrium under uncertainty," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 183-209, November.
    3. Zimper, Alexander, 2005. "Equivalence between best responses and undominated," Papers 05-08, Sonderforschungsbreich 504.
    4. Zimper, Alexander, 2004. "Dominance-solvable lattice games," Papers 04-18, Sonderforschungsbreich 504.
    5. 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.
    6. 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.
    7. Xiao Luo & Yi-Chun Chen, 2004. "A Unified Approach to Information, Knowledge, and Stability," Econometric Society 2004 Far Eastern Meetings 472, Econometric Society.
    8. 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.
    9. Zimper, Alexander, 2004. "On the Existence of Strategic Solutions for Games with Security- and Potential Level Players," Sonderforschungsbereich 504 Publications 04-04, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    10. Alexander Zimper, 2007. "A fixed point characterization of the dominance-solvability of lattice games with strategic substitutes," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 107-117, September.
    11. Lo, Kin Chung, 2007. "Sharing beliefs about actions," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 123-133, March.
    12. Dominiak, Adam & Lee, Min Suk, 2017. "Coherent Dempster–Shafer equilibrium and ambiguous signals," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 42-54.
    13. Alexander Zimper, 2007. "Strategic games with security and potential level players," Theory and Decision, Springer, vol. 63(1), pages 53-78, August.
    14. Roman Kozhan, 2011. "Non-additive anonymous games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 215-230, May.
    15. Lo, Kin Chung, 2006. "Agreement and stochastic independence of belief functions," Mathematical Social Sciences, Elsevier, vol. 51(1), pages 1-22, January.
    16. 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.
    17. 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.
    18. 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.
    19. 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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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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