“Agreeing to Disagree ” Type Results under Ambiguity

In this paper we characterize the conditions under which it is impossible for non-Bayesian agents to “agree to disagree ” on their individual decisions. The agents are Choquet expected utility maximizers in the spirit of Schmeidler (1989, Econometrica 57, 571-587). Under the assumption of a common prior capac-ity distribution, it is shown that whenever each agent’s information partition is composed of unambiguous events in the sense of Nehring (1999, Mat. Soc. Sci. 38, 197-213), then it is impossible that the agents disagree on common knowl-edge decisions, whether they are either posterior capacities or posterior Choquet expectations. Conversely, an agreement on posterior Choquet expectations- but not on posterior capacities- implies that each agent’s private information con-sists of Nehring-unambiguous events. These results indicate that under ambi-guity- contrary to the standard Bayesian framework- asymmetric information matters and can explain differences in common knowledge decisions due to the ambiguous nature of agents ’ private information