6,445 research outputs found
Every hierarchy of beliefs is a type
When modeling game situations of incomplete information one usually considers
the players' hierarchies of beliefs, a source of all sorts of complications.
Hars\'anyi (1967-68)'s idea henceforth referred to as the "Hars\'anyi program"
is that hierarchies of beliefs can be replaced by "types". The types constitute
the "type space". In the purely measurable framework Heifetz and Samet (1998)
formalize the concept of type spaces and prove the existence and the uniqueness
of a universal type space. Meier (2001) shows that the purely measurable
universal type space is complete, i.e., it is a consistent object. With the aim
of adding the finishing touch to these results, we will prove in this paper
that in the purely measurable framework every hierarchy of beliefs can be
represented by a unique element of the complete universal type space.Comment: 19 page
Generalized Descents and Normality
We use Janson's dependency criterion to prove that the distribution of
-descents of permutations of length converge to a normal distribution as
goes to infinity. We show that this remains true even if is allowed to
grow with , up to a certain degree.Comment: 7 page
- …