Knowledge spaces with arbitrarily high rank
A Heifetz, D Samet - Games and Economic Behavior, 1998 - Elsevier
The class of probabilistic belief spaces (Harsanyi, 1967–68, Man. Sci., 14,159–182, 320–
324, 486–502) contains auniversal space, into which every other belief space can be
mapped in a unique way by a belief morphism. We show that there is no analogous
universal space in the class of knowledge spaces. To show this we define therankof a
knowledge space, which is the ordinality of the most complicated descriptions of knowledge
in the space. We then show that a knowledge space can be mapped by a knowledge …
324, 486–502) contains auniversal space, into which every other belief space can be
mapped in a unique way by a belief morphism. We show that there is no analogous
universal space in the class of knowledge spaces. To show this we define therankof a
knowledge space, which is the ordinality of the most complicated descriptions of knowledge
in the space. We then show that a knowledge space can be mapped by a knowledge …