Agreeing to disagree with generalised decision functions

We develop a framework that allows us to emulate standard results from the “agreeing to disagree” literature with generalised decision functions (e.g. Bacharach (1985)) in a manner the avoids known incoherences pointed out by Moses and Nachum (1990). Avoiding the incoherences requires making some sacrifices: For example, we must require the decision functions to be independent of interactive information, and, the language in which the states are described must be “rich” - in some well-defined sense. Using weak additional assumptions, we also extend all previous results to allow agents to base their decisions on possibly false information. Finally, we provide agreement theorems in which the decision functions are not required to satisfy the Sure-Thing Principle (a central assumption in the standard results).