Subjective probability, confidence, and Bayesian updating

I define subjective probabilities for an ambiguity averse agent who is given an exogenous information set containing the true probability law on the state space S. The agent in my model evaluates every uncertain prospect via a mixture of the least favorable scenario in and her unique subjective belief p. This parametric utility structure is characterized by four standard axioms-order, continuity, monotonicity, and Independence-where the last two conditions are modified via the information set . Any pair of preferences and in my model can be compared in terms of confidence-the weights attached to the subjective beliefs and , respectively. The corresponding behavioral condition extends Epstein's comparative ambiguity aversion that leaves some rankings and unrelated. Moreover, I relax the well-known dynamic consistency principle and characterize the Bayesian updating rule for the belief p conditional on any non-null event in S.