Ex Post Strategy-Proofness

Ex post strategy-proofness (ESP) extends the concept of strategy-proofness to settings with interdependent values. ESP requires that truthful reporting is always optimal for every agent, regardless of the strategies and types of other agents. We characterize the class of social choice functions implementable by ESP mechanisms with transfers. For a broad class of environments, including single-good auctions, implementability is jointly characterized by two conditions: (1) Monotonicity, requiring that “higher” types induce “higher” alternatives; and (2) Screenability, requiring that types which are “entangled” must be treated identically, where entanglement becomes increasingly restrictive as types become denser or preference interdependence strengthens. For general settings, we establish that implementability is equivalent to a generalized cyclical monotonicity condition, or equivalently, to an optimality condition derived from an induced matching problem between types and alternatives.