# Maxmin under risk

## Author

Listed:
• 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.

## Suggested Citation

• Fabio Maccheroni, 2002. "Maxmin under risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 823-831.
• 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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## Citations

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Cited by:

1. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
2. 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.
3. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
4. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
5. 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.
6. repec:spr:joecth:v:63:y:2017:i:4:d:10.1007_s00199-016-0972-5 is not listed on IDEAS
7. Evren, Özgür, 2014. "Scalarization methods and expected multi-utility representations," Journal of Economic Theory, Elsevier, vol. 151(C), pages 30-63.
8. Nascimento, Leandro, 2011. "Zhou’s aggregation theorems with multiple welfare weights," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 654-658.
9. Simone Cerreia Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Stochastic Dominance Analysis without the Independence Axiom," Working Papers 549, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
10. Leandro Nascimento & Gil Riella, 2013. "Second-order ambiguous beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 1005-1037, April.
11. 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.
12. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2017. "Mixed extensions of decision problems under uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 827-866, April.

### Keywords

Expected utility; Minimum expected utility; Nonexpected utility.;

### JEL classification:

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

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