Purification, Saturation and the Exact Law of Large Numbers

Wang, Jianwei and Zhang, Yongchao (2010): Purification, Saturation and the Exact Law of Large Numbers.

Abstract

Purification results are important in game theory and statistical decision theory. The purpose of this paper is to prove a general purification theorem that generalizes many authors' 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Exact law of large numbers, Fubini extension, Incomplete information, Purification, Saturated probability space
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General

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