Rationalizable Incentives: Interim Rationalizable Implementation of Correspondences

Résumé : The paper studies the interim rationalizable implementation of social choice sets with a Cartesian product structure, a leading example thereof being ex-post efficiency. Setwise incentive compatibility, a condition much weaker than Bayesian incentive compatibility (BIC), is shown to be necessary for implementation in our sense. Setwise IC enforces incentives flexibly within the entire correspondence, instead of the pointwise enforcement entailed by BIC. Sufficient conditions, while based on the existence of dominant-strategy SCFs in the correspondence, are shown to be permissive to allow the implementation of ex-post efficiency in settings where equilibrium implementation fails. We remark that all our mechanisms are well behaved, in the sense that best responses always exist.