Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies

This paper investigates rationalizable implementation of social choice sets (SCSs) in incomplete information environments. We identify rationalizable incentive compatibility (RIC) as its key condition, argue by means of example that RIC is strictly weaker than the standard Bayesian incentive compatibility (BIC), and show that RIC reduces to BIC when we only consider single-valued SCSs (i.e., social choice functions or SCFs). We next identify additional necessary conditions and, essentially closing the gap between necessity and sufficiency, obtain a sufficiency result for rationalizable implementation in general environments. We also characterize a well-studied class of economic environments in which RIC is essentially the only condition needed for rationalizable implementation. Considering SCFs, we show that interim rationalizable monotonicity, found in the literature, is not necessary for rationalizable implementation, as had been previously claimed.