A revelation principle for obviously strategy-proof implementation

We consider probabilistic versions of obviously strategy-proof implementation (Li, 2017) for stochastic rules, and provide an algorithm involving several ideas from the literature (Ashlagi and Gonczarowski, 2018; Pycia and Troyan, 2016; Bade and Gonczarowski, 2017) that converts any such implementation into a randomized round table implementation, where the administrator randomly selects a game form in which agents take turns making public announcements about their private information (Theorem 1). We provide an analogous algorithm for sure implementation of deterministic rules (Theorem 2); this builds on related results from the literature by (i) relaxing all recall requirements, (ii) allowing randomization by the agents, and (iii) allowing all game trees for which choices determine plays (Alós-Ferrer and Ritzberger, 2016). We discuss a variety of implications and related topics.