On games with incomplete information and the Dvoretsky–Wald–Wolfowitz theorem with countable partitions |
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Authors: | M Ali Khan Kali P Rath |
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Institution: | 1. Department of Economics, The Johns Hopkins University, Baltimore, MD 21218, United States;2. Department of Economics, National University of Singapore, 1 Arts Link, Singapore 117570, Singapore;3. Department of Economics and Econometrics, University of Notre Dame, Notre Dame, IN 46556, United States |
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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. |
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Keywords: | C07 DO5 |
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