# Eliciting ambiguity aversion in unknown and in compound lotteries: a smooth ambiguity model experimental study

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## Abstract

Coherent-ambiguity aversion is defined within the (Klibanoff et al., Econometrica 73:1849–1892, 2005) smooth-ambiguity model (henceforth *KMM*) as the combination of choice-ambiguity and value-ambiguity aversion. Five ambiguous decision tasks are analyzed theoretically, where an individual faces two-stage lotteries with binomial, uniform, or unknown second-order probabilities. Theoretical predictions are then tested through a 10-task experiment. In (unambiguous) tasks 1–5, risk aversion is elicited through both a portfolio choice method and a *BDM* mechanism. In (ambiguous) tasks 6–10, choice-ambiguity aversion is elicited through the portfolio choice method, while value-ambiguity aversion comes about through the *BDM* mechanism. The behavior of over 75 % of classified subjects is in line with the *KMM* model in all tasks 6–10, independent of their degree of risk aversion. Furthermore, the percentage of coherent-ambiguity-averse subjects is lower in the binomial than in the uniform and in the unknown treatments, with only the latter difference being significant. The most part of coherent-ambiguity-loving subjects show a high risk aversion.

## Keywords

Coherent-ambiguity aversion Value-ambiguity aversion Choice-ambiguity aversion Smooth ambiguity model Binomial distribution Uniform distribution Unknown urn## JEL Classification

D81 D83 C91## Notes

### Acknowledgments

The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013) Grant Agreement No. 230589. G. Attanasi gratefully acknowledges financial support by the Chair Georges Meyer in Mathematical Economics at Jean-Jacques Laffont Foundation (TSE). N. Pace gratefully acknowledges financial support by the Swiss&Global and Fondazione Ca’ Foscari. The authors gratefully thank Michèle Cohen, Sandrine Spaeter, Lorenzo Vantaggiato, participants at the 15th Conference on the Foundations and Applications of Utility, Risk and Decision Theory at Georgia State University in Atlanta, at the Workshop on New Developments in Decision Making under Uncertainty at Université de Cergy-Pontoise, and at a Cournot seminar at University of Strasbourg for their useful comments and suggestions.

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