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Finitely additive beliefs and universal type spaces

AuthorsMeier, M.
Issue Date2006
PublisherInstitute of Mathematical Statistics
CitationAnnals of Probability 34(1): 386-422 (2006)
AbstractThe 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 sub-sets of the spaces are required to be measurable, then there is no universal type space. © Institute of Mathematical Statistics.
Identifiersdoi: 10.1214/009117905000000576
issn: 0091-1798
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