Equivalence of Nash implementability and robust implementability with incomplete information

This paper is concerned with the design of robust mechanisms which are applicable to a wide class of possible information structures of agents. We examine a society consisting of several groups such that (i) there are at least three agents in each group; and (ii) each agent knows the preferences of the agents in his group but has incomplete information about the preferences of the agents outside his group. We show that for a large class of information structures, a social choice set (SCS) is implementable for each possible information structure if and only if it is Nash implementable. In other words, the class of robustly implementable SCS's is identical to the class of implementable SCS's in the complete information setting.This paper is a substantially revised version of a chapter of my dissertation submitted to the University of Rochester (Yamato [25]). I thank Professor William Thomson for his invaluable advice and suggestions. Detailed comments and suggestions of an anonymous referee were very helpful for further revision of the paper. I also acknowledge comments from Professors Randall Calvert, Luis Corchon, Glenn MacDonald, Eric Maskin, Lionel McKenzie, Ryo-Ichi Nagahisa, Koji Okuguchi, Ignacio Ortuño-Ortin, Tatsuyoshi Saijo, Ken-Ichi Shimomura, Tomas Sjöström, Yoshikatsu Tatamitani, and seminar participants at Harvard University, the 1992 Meeting of Kobe Summer Seminar in Economics of Organization and Game Theory, Tokyo Metropolitan University, and Toyama University. This work was supported in part by the Ministry of Education in Japan, the Nomura Foundation for the Social Sciences, and the Tokyo Center for Economic Research.