A revelation principle for obviously strategy-proof implementation

We prove that if a stochastic (social choice) rule has an obviously strategy-proof (OSP) implementation (Li, 2016), then it has such an implementation through a randomized round table mechanism, where the administrator randomly selects a game form in which the agents take turns making public announcements about their private information. When restricted to deterministic rules, our result improves upon other recent revelation principles by relaxing all recall requirements and by allowing all game trees compatible with normal forms (Alós-Ferrer and Ritzberger, 2016); we also establish robustness to player randomization using novel solution concepts involving mixed strategies and behavioral strategies. We use our result to provide a justification for ordinal mechanisms in the spirit of Carroll (2017), and we provide a simple characterization of the deterministic rules with OSP-implementations using deterministic round table mechanisms and ordinary strategy-proofness.