Interdependent Preferences and Strategic Distinguishability

We identify a universal type space of possible interdependent (expected utility) preferences of a group of agents satisfying two criteria. First, a type consists of a "detail free" description, in a natural language, of the agents' interdependent preferences. Second, distinct types in the universal type space must be "strategically distinguishable" in the sense that there must exist a mechanism where those types are guaranteed to behave differently in equilibrium. Our results generalize and unify results of Abreu and Matsushima (1992b) (who characterized strategic distinguishability on fixed finite type spaces) and Dekel, Fudenberg, and Morris (2006), (2007) (who characterized strategic distinguishability on type spaces without preference uncertainty and thus without interdependent preferences).