Safe implementation

Implementation theory is concerned with the existence of mechanisms in which, at each state of the world, all equilibria result in outcomes that are within a given Social Choice Correspondence (SCC). But if agents make mistakes, if their preferences or the solution concept are misspecified, or if the designer is limited in what can be used as punishments, then it may be desirable to insist that also deviations result in `acceptable' outcomes. Safe Implementation adds this extra requirement to standard implementation. Our primitives therefore also include an Acceptability Correspondence, which like the SCC maps states of the world to sets of allocations. When the underlying solution concept is Nash Equilibrium, we identify necessary and sufficient conditions (namely, Comonotonicity and Safe No-Veto) that restrict the joint behavior of the SCC and of the Acceptability Correspondence, and that generalize Maskin’s (1977) conditions. In relevant economic applications, these conditions can be quite permissive. But in `rich' preference domains, Safe Implementation is impossible, regardless of the solution concept.