Finitely additive beliefs and universal type spaces

• 成果类型: Article
• 署名作者: Meier, M
• 署名单位: Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Institut d'Analisi Economica (IAE)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000576
• 发表日期: 2006
• 页码: 386-422
• 关键词: knowledge

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 (kappa-measurability, for some fixed regular cardinal K), 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.