“Agreeing to Disagree ” Type Results under Ambiguity

In this paper we characterize conditions under which it is impossible that non-Bayesian agents “agree to disagree ” on their individual decisions. The agents are Choquet expected utility maximizers in the spirit of Schmeidler (1989, Econo-metrica 57, 571-587). Under the assumption of a common prior capacity distri-bution, it is shown that whenever each agent’s information partition is made up of unambiguous events in the sense of Nehring (1999, Mat. Soc. Sci. 38, 197-213), then it is impossible that the agents disagree on the common knowledge decisions, whether they are posterior capacities or posterior Choquet expecta-tions. Conversely, an agreement on posterior Choquet expectations- but not on posterior capacities- implies that each agent’s private information consists of Nehring-unambiguous events. These results indicate that under ambiguity-contrary to the standard Bayesian framework- asymmetric information matters and can explain differences in common knowledge decisions due to the ambigu-ous nature of agents ’ private information