Interim Rationalizable Implementation of Functions

Bravo Working Paper # 2020-023

51 Pages Posted: 12 Dec 2020

See all articles by Takashi Kunimoto

Takashi Kunimoto

Brown University - Department of Economics

Rene Saran

University of Cincinnati - Department of Economics

Roberto Serrano

Brown University

Date Written: October 16, 2020

Abstract

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

Kunimoto, Takashi and Saran, Rene and Serrano, Roberto, Interim Rationalizable Implementation of Functions (October 16, 2020). Bravo Working Paper # 2020-023 , Available at SSRN: https://ssrn.com/abstract=3713463 or http://dx.doi.org/10.2139/ssrn.3713463

Takashi Kunimoto

Brown University - Department of Economics ( email )

64 Waterman Street
Providence, RI 02912
United States
401-863-2735 (Phone)
401-863-1970 (Fax)

Rene Saran

University of Cincinnati - Department of Economics ( email )

Carl H. Lindner Hall 2925 Campus Green Drive
PO Box 0371
Cincinnati, OH 45221-0211
United States

Roberto Serrano (Contact Author)

Brown University ( email )

64 Waterman Street
Providence, RI 02912
United States
401-863-1036 (Phone)
401-863-1970 (Fax)

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