# An axiomatization of Choquet expected utility with cominimum independence

## Author

Listed:
• 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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File URL: http://hdl.handle.net/10.1007/s11238-013-9411-2

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## References listed on IDEAS

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1. 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.
2. Asano, Takao, 2006. "Portfolio inertia under ambiguity," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 223-232, December.
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. Jürgen Eichberger & David Kelsey, 1999. "E-Capacities and the Ellsberg Paradox," Theory and Decision, Springer, vol. 46(2), pages 107-138, April.
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," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 579-608.
7. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-1169, September.
8. Kajii, Atsushi & Kojima, Hiroyuki & Ui, Takashi, 2007. "Cominimum additive operators," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 218-230, February.
9. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
10. 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.
Full references (including those not matched with items on IDEAS)

### Keywords

Cominimum additivity; Cominimum independence; Choquet expected utility; Multi-prior expected utility; Core ; E-capacity expected utility;

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