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Title: On games with incomplete information and the Dvoretsky-Wald-Wolfowitz theorem with countable partitions
Authors: Khan, M.A. 
Rath, K.P.
Keywords: Atomless games
Countably infinite actions
Countably infinite partitions
Independent private information
The DWW theorem
Issue Date: 2009
Citation: Khan, M.A., Rath, K.P. (2009). On games with incomplete information and the Dvoretsky-Wald-Wolfowitz theorem with countable partitions. Journal of Mathematical Economics 45 (12) : 830-837. ScholarBank@NUS Repository.
Abstract: 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. © 2009 Elsevier B.V. All rights reserved.
Source Title: Journal of Mathematical Economics
ISSN: 03044068
DOI: 10.1016/j.jmateco.2009.06.003
Appears in Collections:Staff Publications

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