Hierarchies of ambiguous beliefs

We present a theory of interactive beliefs analogous to Mertens and Zamir [31] and Brandenburger and Dekel [10] that allows for hierarchies of ambiguity. Each agent is allowed a compact set of beliefs at each level, rather than just a single belief as in the standard model. We propose appropriate definitions of coherency and common knowledge for our types. Common knowledge of coherency closes the model, in the sense that each type homeomorphically encodes a compact set of beliefs over the others’ types. This space universally embeds every implicit type space of ambiguous beliefs in a beliefs-preserving manner. An extension to ambiguous conditional probability systems [4] is presented. The standard universal type space and the universal space of compact continuous possibility structures are epistemically identified as subsets. JEL classification: C72; D81