Uncertainty in Beliefs and Preferences: Conditions for Optimal Alternatives

Bayes decision problems require subjective elicitation of inputs: beliefs and preferences. Elicitation methods are far from simple, and elicited quantities cannot perfectly represent the judgements of the Decision Maker. Several foundations suggest overlaying this problem using robust approaches. In these models, beliefs are modelled by a class of probability distributions, and preferences by a class of loss functions. Then we have a Pareto order. So, the solution concept is an efficient set. In this paper, we deal with the problem of existence of a solution. Moreover, we study the relations between Bayes actions and nondominated ones.