Choquet expected utility and never best choice
研究了在给定一组容量(描述状态不确定性)和一组行动时,一个行动何时永远不会成为最佳选择,即对每个容量都存在另一个行动具有更高的Choquet期望效用。
Given a set of capacities describing uncertainty over a set of states, and a set of acts, the question is considered when an act is never a best choice, i.e., when for every capacity there is another act with higher Choquet expected utility. This question is answered for several sets of capacities, distinguished by their supports, where the focus is on four different definitions of a support. One consequence of the analysis is that an act is never a best choice against the set of all capacities if and only if it is strictly dominated by a convex combination of the comonotonized versions of the other acts. This result can be seen as the counterpart of the analogous result for additive capacities, such as mixed strategies in games.