Non-well-founded-type spaces

In a Harsanyi-types space, states become circular, self-referring objects if one tries to make the types an explicit part of the states' structure. 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 uncertainties. This non-well-founded version is isomorphic to a beliefs subspace of the Mertens - Zamir hierarchic construction, although its definition involves no inductive process. Journal of Economic Literature Classification Number: D82.