A new framework for the Bayesian analysis of single-stage decision problems with imprecise utilities

A mathematical framework to model the Bayesian analysis of single-stage decision problems with imprecise utilities is proposed. The main advantage of this model with respect to previous models for such a problem, is that product measurability of the utility function is not necessary, since this model involves iterated expectations instead of an integral over a product space. Conditions for the equivalence between the extensive and normal forms of the Bayesian analysis, within the proposed framework, are obtained. The model is illustrated with an example in which the utility function is not product measurable.