Decision making under uncertainty using imprecise probabilities

Various ways for decision making with imprecise probabilities (admissibility, maximal expected utility, maximality, E-admissibility, $\Gamma$-maximax, $\Gamma$-maximin, all of which are well-known from the literature) are discussed and compared. We generalize a well-known sufficient condition for existence of optimal decisions. A simple numerical example shows how these criteria can work in practice, and demonstrates their differences. Finally, we suggest an efficient approach to calculate optimal decisions under these decision criteria.