FINITELY ADDITIVE BELIEFS AND UNIVERSAL TYPE SPACES1 BY MARTIN MEIER Instituto de Análisis Económico, CSIC
ثبت نشده
چکیده
The probabilistic type spaces in the sense of Harsanyi [Management Sci. 14 (1967/68) 159–182, 320–334, 486–502] are the prevalent models used to describe interactive uncertainty. In this paper we examine the existence of a universal type space when beliefs are described by finitely additive probability measures. We find that in the category of all type spaces that satisfy certain measurability conditions (κ-measurability, for some fixed regular cardinal κ), there is a universal type space (i.e., a terminal object) to which every type space can be mapped in a unique beliefs-preserving way. However, by a probabilistic adaption of the elegant sober-drunk example of Heifetz and Samet [Games Econom. Behav. 22 (1998) 260–273] we show that if all subsets of the spaces are required to be measurable, then there is no universal type space.
منابع مشابه
Finitely Additive Beliefs and Universal Type Spaces
In this paper we examine the existence of a universal (to be precise: terminal) type space when beliefs are described by finitely additive probability measures. We find that in the category of all type spaces that satisfy certain measurability conditions (κ-measurability, for some fixed regular cardinal κ), there is a universal type space (i.e. a terminal object, that is a type space to which e...
متن کاملHierarchies of beliefs for compact possibility models
In this paper, we construct a universal type space for a class of possibility models by imposing topological restrictions on the players’ beliefs. Along the lines of Mertens and Zamir [International Journal of Game Theory, 14 (1985) 1] or Brandenburger and Dekel [Journal of Economic Theory 59 (1993) 189], we show that the space of all hierarchies of compact beliefs that satisfy common knowledge...
متن کاملEvery hierarchy of beliefs is type
Any model of incomplete information situations has to consider the players’ hierarchies of beliefs, which can make the modeling very cumbersome. Harsányi [12] suggested that the hierarchies of beliefs can be replaced by types, i.e., a type space can substitute for the hierarchies of beliefs (henceforth Harsányi program). In the purely measurable framework Heifetz and Samet [15] formalized the c...
متن کاملEvery hierarchy of beliefs is a type
Any model of incomplete information situations has to consider the players' hierarchies of beliefs, which can make the modeling very cumbersome. Harsányi [12] suggested that the hierarchies of beliefs can be replaced by types, i.e., a type space can substitute for the hierarchies of beliefs (henceforth Harsányi program). In the purely measurable framework Heifetz and Samet [15] formalized the c...
متن کاملWorking Paper Series Unawareness , Beliefs , and Speculative Trade
We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for potential applications of asymmetric unawareness. Applying our unawareness belief structures, we show that the common prior assumption is too weak to rule out speculative trade in all states. Yet, we prove a generalized “No-speculative-trade” theorem according to which...
متن کامل