A Revelation Principle for Rationalizability

2026-07-23

AI Summary

This study addresses the limitations of existing interim rationalizability frameworks, which fail to effectively reveal preferences due to their neglect of higher-order belief information. By constructing a complete hierarchy of surviving action sets and imposing layer-wise obedience constraints, the paper establishes a self-enforcing distribution over states and higher-order beliefs under the condition that best-response regions are convex. It innovatively introduces a payoff-structure-dependent direct representation method, employing a finite set of labels to induce a convex partition of best-response regions for any finite payoff structure, thereby preserving consistency with the classical rationalizability hierarchy. In particular, the work demonstrates that binary actions and a class of ordered payoff structures yield polyhedral best-response regions and provides a finite-label direct revelation representation for general finite payoff structures.

Abstract

We establish a revelation principle for interim correlated rationalizability. Revealing only terminal rationalizable action sets fails because it discards information on higher order beliefs that generated them. We therefore use the full hierarchy of surviving action sets. When exact best-response regions are convex, the induced distribution over states and hierarchies implements itself and is characterized by level-by-level obedience constraints. All binary-action payoff structures and a class of ordered payoff structures with interval best-response sets are polyhedral. For arbitrary finite payoff structures, we partition exact best-response regions into finitely many convex cells and tag each hierarchy level by its cell. Tagged hierarchies satisfy analogous obedience constraints and project onto the ordinary rationalizability hierarchy. Thus every finite payoff structure admits a payoff-structure-dependent direct representation with finitely many tags at each level.

Problem

• revelation principle
• rationalizability
• higher-order beliefs
• best-response regions
• payoff structures

Innovation

• revelation principle
• interim correlated rationalizability
• hierarchy of beliefs
• convex best-response regions
• finite payoff structures