NON-WELL-FOUNDED-TYPE SPACES

In a Harsanyi-types space, states become circular, self-referring obje cts if one tries to make the types an explicit part of the states' str ucture. To make such a definition rigorous, we suggest the use of non- well-founded sets that may be members of themselves, members of their members. etc. We show how to define the non-well-founded version of a types space in a way that preserves nature and the mutual uncertaintie s. This non-well-founded version is isomorphic to a beliefs subspace o f the Mertens-Zamir hierarchic construction, although its definition i nvolves no inductive process. Journal of Economic Literature Classific ation Number: D82. (C) 1996 Academic Press, lnc.