完全可加信念与泛型空间
Finitely additive beliefs and universal type spaces
摘要：
概率型空间在意义上的海萨尼[管理科学。14（1967/68）159- 182，320- 334，486- 502]是用来描述交互不确定性的流行模型。在本文中，我们研究的存在性的普遍类型空间时，信念是描述的可加性概率测度。我们发现，在所有满足一定可测性条件（$κ$ -可测性，对于某个固定的正则基数$κ$）的型空间的范畴中，存在一个泛型空间（即，终对象），每个类型空间可以以唯一的置信度保持方式映射到该最终对象。然而，通过对海菲兹和萨米特[游戏经济学]的优雅清醒醉酒例子的概率改编。举止得体22（1998）260- 273]我们证明了如果要求空间的所有子集都是可测的，则不存在泛类型空间。
英文摘要：
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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