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January 2006 Finitely additive beliefs and universal type spaces
Martin Meier
Ann. Probab. 34(1): 386-422 (January 2006). DOI: 10.1214/009117905000000576


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.


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Martin Meier. "Finitely additive beliefs and universal type spaces." Ann. Probab. 34 (1) 386 - 422, January 2006.


Published: January 2006
First available in Project Euclid: 17 February 2006

zbMATH: 1161.91009
MathSciNet: MR2206351
Digital Object Identifier: 10.1214/009117905000000576

Primary: 28E , 91A35 , 91A40

Keywords: Finitely additive probability measures , games of incomplete information , Harsanyi type spaces , universal type space , κ-measurability

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 1 • January 2006
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