Rationalizable Implementation of Correspondences∗ Takashi Kunimotoyand Roberto Serranoz This Version: May 2016 Abstract We come close to characterizing the class of social choice correspon- dences that are implementable in rationalizable strategies. We identify a new condition, which we call set-monotonicity, and show that it is necessary and almost sufficient for rationalizable implementation. Set-monotonicity is much weaker than Maskin monotonicity, which is the key condition for Nash implementation and which also had been shown to be necessary for rationalizable implementation of social choice functions. Set-monotonicity reduces to Maskin monotonicity in the case of functions. We conclude that the conditions for rationalizable implementation are not only starkly differ- ent from, but also much weaker than those for Nash implementation, when we consider social choice correspondences. JEL Classification: C72, D78, D82. Keywords: Complete information, implementation, Maskin monotonicity, rationalizability, set-monotonicity, social choice correspondence. 1 Introduction The design of institutions to be used by rational agents has been an important research agenda in economic theory. As captured by the notion of Nash equilib- rium, rationality is encapsulated in two aspects: these are (i) the best responses of agents to their beliefs, and (ii) that those beliefs are correct, the so-called rational ∗Financial support from the Japan Society for the Promotion of Science (24330078, 25780128) (Kunimoto) is gratefully acknowledged. All remaining errors are our own. ySchool of Economics, Singapore Management University, 90 Stamford Road, Singapore 178903;
[email protected] zDepartment of Economics, Brown University, Providence, RI 02912, U.S.A.; roberto
[email protected] 1 expectations assumption. One can drop the latter and retain the former, moving then into the realm of rationalizability.