Universal Divinity

Universal divinity (also called D2) is the strongest of the belief-based equilibrium refinements introduced by Banks and Sobel (1987). A type θ is eliminated by universal divinity at an off-path message m if, for every other type θ′, the set of receiver responses that would make m profitable for θ is a subset of the set that would make it profitable for θ′:

D(θ, m) ⊆ D(θ′, m) for all θ′ ≠ θ

Where the divinity criterion (D1) eliminates a type only when there exists some other type with a strictly larger beneficial-response set, universal divinity eliminates a type whenever its beneficial-response set is weakly smaller than every other type's. This makes D2 strictly stronger than D1 and often yields unique predictions in signaling games where D1 permits multiplicity.

Universal divinity is closely related to the Never-a-Weak-Best-Response condition and to the broader concept of strategic stability developed by Kohlberg and Mertens (1986). In many applications, D2 selects the Riley outcome in signaling games — the most efficient separating equilibrium — though it can also eliminate all equilibria in some games, leaving no D2-perfect prediction at all.

Universal divinity is the theorist's dream and the experimentalist's nightmare: a refinement so strong that it often yields unique predictions, but so demanding that no human subject has ever been observed satisfying it. The question is not whether D2 is "correct" but whether any concept this strong can claim to describe anything other than the limiting behavior of infinitely rational agents. If universal divinity is the right concept, then most of what humans do in strategic settings is not merely suboptimal — it is incomprehensible.