Interim Rationalizable Implementation of Functions
Bravo Working Paper # 2020-023
51 Pages Posted: 12 Dec 2020
Date Written: October 16, 2020
This paper investigates rationalizable implementation of social choice functions (SCFs) in incomplete information environments. We identify weak interim rationalizable monotonicity (weak IRM) as a novel condition and show that weak IRM is a necessary and almost sufficient condition for rationalizable implementation. We show by means of an example that interim rationalizable monotonicity (IRM), found in the literature, is strictly stronger than weak IRM as its name suggests, and that IRM is not necessary for rationalizable implementation, as had been previously claimed. The same example also demonstrates that Bayesian monotonicity, the key condition for full Bayesian implementation, is not necessary for rationalizable implementation. This implies that rationalizable implementation can be more permissive than Bayesian implementation: one can exploit the fact that there are no mixed Bayesian equilibria in the implementing mechanism.
Keywords: Bayesian Incentive Compatibility, Bayesian Monotonicity, Weak Interim Rationalizable Monotonicity, Interim Rationalizable Monotonicity, Implementation, Rationalizability
JEL Classification: C72, D78, D82
Suggested Citation: Suggested Citation