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An axiomatization of Choquet expected utility with cominimum independence

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  • Takao Asano

  • Hiroyuki Kojima

Abstract

This paper proposes a class of independence axioms for simple acts. By introducing the $${\mathcal {E}}$$ E -cominimum independence axiom that is stronger than the comonotonic independence axiom but weaker than the independence axiom, we provide a new axiomatization theorem of simple acts within the framework of Choquet expected utility. Furthermore, in order to provide the axiomatization of simple acts, we generalize Kajii et al. (J Math Econ 43:218–230, 2007 ) into an infinite state space. Our axiomatization theorem relates Choquet expected utility to multi-prior expected utility through the core of a capacity that is explicitly derived within our framework. Our result in this paper also derives Gilboa (Econometrica 57:1153–1169, 1989 ), Eichberger and Kelsey (Theory Decis 46:107–140, 1999 ), and Rohde (Soc Choice Welf 34:537–547, 2010 ) as a corollary. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Takao Asano & Hiroyuki Kojima, 2015. "An axiomatization of Choquet expected utility with cominimum independence," Theory and Decision, Springer, vol. 78(1), pages 117-139, January.
    • Handle: RePEc:kap:theord:v:78:y:2015:i:1:p:117-139
    DOI: 10.1007/s11238-013-9411-2
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    References listed on IDEAS

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    1. Asano, Takao, 2006. "Portfolio inertia under ambiguity," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 223-232, December.
    2. Zhang, Jiankang, 1999. "Qualitative probabilities on [lambda]-systems," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 11-20, July.
    3. Kirsten Rohde, 2010. "A preference foundation for Fehr and Schmidt’s model of inequity aversion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 537-547, April.
    4. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(3), pages 579-608.
    7. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    8. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-1169, September.
    9. Kajii, Atsushi & Kojima, Hiroyuki & Ui, Takashi, 2007. "Cominimum additive operators," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 218-230, February.
    10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    11. Jürgen Eichberger & David Kelsey, 1999. "E-Capacities and the Ellsberg Paradox," Theory and Decision, Springer, vol. 46(2), pages 107-138, April.
    12. 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.
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    Cited by:

    1. Takao Asano & Hiroyuki Kojima, 2019. "Consequentialism and dynamic consistency in updating ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 223-250, July.

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