The von Neumann/Morgenstern approach to ambiguity
| Title: | The von Neumann/Morgenstern approach to ambiguity |
| Author: | Dumav, Martin |
| Abstract: | An outcome is ambiguous if it is an incomplete description of the probability distribution over consequences. An `incomplete description' is identified with the set of probabilities that satisfy the incomplete description. A choice problem is uncertain if the decision maker is choosing between distributions, and is ambiguous if the decision maker is choosing between sets of probabilities. The von Neumann/Morgenstern approach to uncertain choice problems uses a continuous linear function on probabilities. This paper develops the theory of ambiguous choice problems as a continuous, linear functions on closed convex sets of probabilities. This delivers: a framework encompassing most of the extant ambiguity averse preferences; a complete separation of attitudes towards risk and attitudes toward ambiguity; and generalizations of rst and second order stochastic dominance rankings to ambiguous decision problem. Quasi-concave preferences on sets that satisfy a restricted betweenness property capture variational preferences. |
| Department: | Mathematics |
| Subject: |
Ambiguity
Decision theory von Neumann/Morgenstern |
| URI: | http://hdl.handle.net/2152/ETD-UT-2011-08-4292 |
| Date: | 2011-08 |
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