# Maxmin under risk

## Author Info

• Fabio Maccheroni

()
(Istituto di Metodi Quantitativi, Università Bocconi, viale Isonzo 25, 20135 Milano, ITALY)

## Abstract

Let $\succsim$ be a continuous and convex weak order on the set of lotteries defined over a set Z of outcomes. Necessary and sufficient conditions are given to guarantee the existence of a set $\mathcal{U}$ of utility functions defined on Z such that, for any lotteries p and q, $p\succsim q \Leftrightarrow \min_{u\in{\mathcal U}}{\Bbb E} _p\left[ u\right] \geq \min_{u\in{\mathcal U}}{\Bbb E} _q\left[ u\right] .$ The interpretation is simple: a conservative decision maker has an unclear evaluation of the different outcomes when facing lotteries. She then acts as if she were considering many expected utility evaluations and taking the worst one.

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## Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 19 (2002)
Issue (Month): 4 ()
Pages: 823-831

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Handle: RePEc:spr:joecth:v:19:y:2002:i:4:p:823-831

Note: Received: January 19, 2000; revised version: December 20, 2000
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## Related research

Keywords: Expected utility; Minimum expected utility; Nonexpected utility.;

Find related papers by JEL classification:

• D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

## References

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## Citations

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Cited by:
1. Nascimento, Leandro, 2011. "Zhou’s aggregation theorems with multiple welfare weights," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 654-658.
2. Simone Cerreia-Vioglio & David Dillenberger & Pietro Ortoleva, 2013. "Cautious Expected Utility and the Certainty Effect," PIER Working Paper Archive 13-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
3. Kraus, Alan & Sagi, Jacob S., 2006. "Inter-temporal preference for flexibility and risky choice," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 698-709, September.
4. Leandro Nascimento & Gil Riella, 2013. "Second-order ambiguous beliefs," Economic Theory, Springer, vol. 52(3), pages 1005-1037, April.
5. Chatterjee, Kalyan & Vijay Krishna, R., 2011. "A nonsmooth approach to nonexpected utility theory under risk," Mathematical Social Sciences, Elsevier, vol. 62(3), pages 166-175.
6. Babacar Seck & Laetitia Andrieu & Michel De Lara, 2012. "Parametric multi-attribute utility functions for optimal profit under risk constraints," Theory and Decision, Springer, vol. 72(2), pages 257-271, February.

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