Gavan, Malachy James and Penta, Antonio (2022) Safe Implementation. TSE Working Paper, n. 22-1369, Toulouse

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Abstract

We introduce Safe Implementation, a notion of implementation that adds to the stan-dard requirements the restriction that deviations from the baseline solution concept induce outcomes that are acceptable. The primitives of Safe Implementation 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 stan-dard notions of implementation, and can accommodate a variety of considerations, including robustness concerns with respect to mistakes in play, model misspecification, behavioral con-siderations, state-dependent feasibility restrictions, limited commitment, etc.
We provide results both for general solution concepts and for the case in which agents’ interaction is modelled by Nash Equilibrium. In the latter case, we identify necessary and suf-ficient conditions (namely, Comonotonicity and safety-no veto) that restrict the joint behavior of the Social Choice and Acceptability Correspondences. These conditions are more stringent than Maskin’s (1978), but coincide with them when the safety requirements are vacuous. We also show that these conditions are quite permissive in important economic applications, such as environments with single-crossing preferences and in problems of efficient allocation of in-divisible goods, but also that Safe Implementation can be very demanding in environments with ‘rich’ preferences, regardless of the underlying solution concept.