Purification, Saturation and the Exact Law of Large Numbers
AbstractPurification 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 22119.
Date of creation: Apr 2010
Date of revision:
Exact law of large numbers; Fubini extension; Incomplete information; Purification; Saturated probability space;
Other versions of this item:
- Jianwei Wang & Yongchao Zhang, 2012. "Purification, saturation and the exact law of large numbers," Economic Theory, Springer, vol. 50(3), pages 527-545, August.
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-02 (All new papers)
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- Michael Greinecker & Konrad Podczeck, 2013. "Purification and Independence," Working Papers 2013-18, Faculty of Economics and Statistics, University of Innsbruck.
- Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2013. "Savage Games: A Theory of Strategic Interaction with Purely Subjective Uncertainty," Risk and Sustainable Management Group Working Papers 151501, University of Queensland, School of Economics.
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