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Purification, saturation and the exact law of large numbers |
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| Authors: | Jianwei Wang Yongchao Zhang |
| Affiliation: | 1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui Province, People??s Republic of China 2. Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore 3. Hausdorff Research Institute for Mathematics, 53115, Bonn, Germany |
| Abstract: | Purification results are important in game theory and statistical decision theory. We prove a new purification theorem that generalizes several earlier results. The key idea of our proof is to make use of the exact law of large numbers. As an application, we show that every mixed strategy in games with finite players, general action spaces and diffused, conditionally independent incomplete information has many strong purifications. |
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