On games with incomplete information and the Dvoretsky–Wald–Wolfowitz theorem with countable partitions

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• 作者：M. Ali Khan ; Kali P. Rath
• 关键词：Atomless games ; Independent private information ; Countably infinite actions ; Countably infinite partitions ; The DWW theorem
• 刊名：Journal of Mathematical Economics
• 出版年：2009
• 出版时间：20 December 2009
• 年：2009
• 卷：45
• 期：12
• 页码：830-837
• 全文大小：248 K

文摘

It has remained an open question as to whether the results of Milgrom–Weber [Milgrom, P.R., Weber, R.J., 1985. Distributional strategies for games with incomplete information. Mathematics of Operations Research 10, 619–632] are valid for action sets with a countably infinite number of elements without additional assumptions on the abstract measure space of information. In this paper, we give an affirmative answer to this question as a consequence of an extension of a theorem of Dvoretzky, Wald and Wolfowitz (henceforth DWW) due to Edwards [Edwards, D.A., 1987. On a theorem of Dvoretsky, Wald and Wolfowitz concerning Liapunov measures. Glasgow Mathematical Journal 29, 205–220]. We also present a direct elementary proof of the DWW theorem and its extension, one that may have an independent interest.