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Non-well-founded-type spaces. (English) Zbl 0860.90045

Summary: 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..

MSC:

91B99 Mathematical economics
03E30 Axiomatics of classical set theory and its fragments
91A99 Game theory
03E47 Other notions of set-theoretic definability
03E65 Other set-theoretic hypotheses and axioms
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