Exactly what happens after the Anscombe-Aumann race? (English) Zbl 1185.91072
Author’s abstract: This paper derives a representation of preferences for a choice theory with vague environments; vague in the sense that the agent does not know the precise lotteries over outcomes conditional on states. Instead, he knows only a possible set of these lotteries for each state. Thus, this paper’s main departure from the standard subjective expected utility model is to relax an assumption about the environment, rather than weakening the axiomatic structure. My model is consistent with the behavior observed in the Ellsberg experiment. It can capture the same type of behavior as the multiple priors models, but can also result in behavior that is different from both the behavior implied by standard subjective expected utility models and the behavior implied by the multiple priors models.
The approach presented in this paper is based on 8 axioms, 10 lemmas and three theorems with the proofs of sufficiency and necessity of axioms, as well as with proofs of lemmas and theorems concentrated in the appendix. All the general concepts are illustrated by seven figures, list of references includes 24 works, but the article does not contain any numerical example illustrating efficiency of the proposed theory.
The approach presented in this paper is based on 8 axioms, 10 lemmas and three theorems with the proofs of sufficiency and necessity of axioms, as well as with proofs of lemmas and theorems concentrated in the appendix. All the general concepts are illustrated by seven figures, list of references includes 24 works, but the article does not contain any numerical example illustrating efficiency of the proposed theory.
Reviewer: Vitali Oscarovich Groppen (Vladikavkaz)
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