Agreement theorem for neo-additive beliefs

In this paper, we extend Aumann's (Ann Stat 4:1236—1239, 1976) probabilistic agreement theorem to situations in which agents' prior beliefs are represented by a common neo-additive capacity. In particular, we characterize the family of updating rules for neo-additive capacities, which are necessary and sufficient for the impossibility of "agreeing to disagree" on the values of posterior capacities as well as on the values of posterior Choquet expectations for binary acts. Furthermore, we show that generalizations of this result to more general acts are impossible.