We introduce Safe Implementation, a framework for implementation theory that adds to the standard requirements the restriction that agents’ deviations induce out- comes that are acceptable. Our primitives therefore include both a Social Choice Correspondence, as standard, and an Acceptability Correspondence, each mapping every state of the world to a subset of allocations. This framework generalizes standard notions of implementation, and can accommodate a variety of questions, including robustness with respect to mistakes in play, behavioral considerations, state-dependent feasibility restrictions, limited commitment, etc. We provide results both for general solution concepts and for Nash Equilibrium. For the latter, we identify necessary and sufficient conditions (namely, Comonotonicity and safety-no veto ) that restrict the joint behavior of the Social Choice and Accept- ability Correspondences, which generalize Maskin’s (1977) conditions. We also show that these conditions are quite permissive in important economic applications, but also that Safe Implementation can be very demanding in environments with ‘rich’ preferences, regardless of the underlying solution concept.
