Rationalizable Implementation of Correspondences

A new condition, which we call uniform monotonicity, is shown to be necessary and almost sufficient for rationalizable implementation of correspondences. Uniform monotonicity is much weaker than Maskin monotonicity and reduces to it in the case of functions. Maskin monotonicity, the key condition for Nash implementation, had also been shown to be necessary for rationalizable implementation of social choice functions. Our conclusion is that the conditions for rationalizable implementation are not only starkly different from but also, much weaker than those for Nash implementation when we consider social choice correspondences. Thus, dropping rational expectations significantly expands the class of rules that can be decentralized by communication-based economic institutions.