20.
The Choquet expected utility model deals with nonadditive probabilities (or capacities). Their dependence on the information
the decision-maker has about the possibility of the events is taken into account. Two kinds of information are examined: interval
information (for instance, the percentage of white balls in an urn is between 60% and 100%) and comparative information (for
instance, the information that there are more white balls than black ones). Some implications are shown with regard to the
core of the capacity and to two additive measures which can be derived from capacities: the Shapley value and the nucleolus.
Interval information bounds prove to be satisfied by all probabilities in the core, but they are not necessarily satisfied
by the nucleolus (when the core is empty) and the Shapley value. We must introduce the constrained nucleolus in order for
these bounds to be satisfied, while the Shapley value does not seem to be adjustable. On the contrary, comparative information
inequalities prove to be not necessarily satisfied by all probabilities in the core and we must introduce the constrained
core in order for these inequalities be satisfied. However, both the nucleolus and the Shapley value satisfy the comparative
information inequalities, and the Shapley value does it more strictly than the nucleolus.
This revised version was published online in June 2006 with corrections to the Cover Date.
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