“Agreeing to disagree” type results under ambiguity

This paper characterizes 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. Whenever each agent’s information partition is composed of unambiguous events in the sense of Nehring (1999), then the agents cannot disagree on the common knowledge decisions, whether these decisions are conditional capacities or conditional Choquet expectations. Conversely, an agreement on conditional Choquet expectations, but not on conditional capacities, implies that each agent’s private information must consist of Nehring-unambiguous events. These results indicate that under ambiguity–contrary to the standard Bayesian framework–asymmetric information matters, and it can explain differences in common knowledge decisions due to the ambiguous nature of the agents’ private information.