Abstract
Foundations are provided for rank-dependent preferences within the popular two-stage framework of Anscombe–Aumann, in which risk and ambiguity feature as distinct sources of uncertainty. We advance the study of attitudes towards ambiguity without imposing expected utility for risk. As a result, in our general model, ambiguity attitude can be captured by non-additive subjective probabilities as under Choquet expected utility or by a specific utility for ambiguity as in recursive expected utility or, if required, by both. The key property for preferences builds on (discrete) rates of substitution which are standardly applied in economics. By demanding consistency for these rates of substitution across events and within or across sources of uncertainty, we obtain a model that nests popular theories for risk and ambiguity. This way, new possibilities for theoretical and empirical analyses of these theories emerge.
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We like to acknowledge the constructive comments of three anonymous referees and the handling editor, which have lead to several improvements. The earlier version titled “Recursive Rank-dependent Utility” has benefitted from discussions and remarks from Edi Karni, Peter Wakker and Chris Wallace. The paper was developed during Mohammed Abdellaoui’s Hallsworth Visiting Professorship at the Univeristy of Manchester.
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Abdellaoui, M., Zank, H. Source and rank-dependent utility. Econ Theory 75, 949–981 (2023). https://doi.org/10.1007/s00199-022-01434-4
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DOI: https://doi.org/10.1007/s00199-022-01434-4
Keywords
- Ambiguity
- Recursive expected utility
- Risk
- Substitution consistency
- Source-dependence
- Source and rank-dependent utility