The Annals of Probability

Finitely additive beliefs and universal type spaces

Martin Meier

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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.

Article information

Ann. Probab., Volume 34, Number 1 (2006), 386-422.

First available in Project Euclid: 17 February 2006

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Zentralblatt MATH identifier

Primary: 91A40: Game-theoretic models 91A35: Decision theory for games [See also 62Cxx, 91B06, 90B50] 28E

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


Meier, Martin. Finitely additive beliefs and universal type spaces. Ann. Probab. 34 (2006), no. 1, 386--422. doi:10.1214/009117905000000576.

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