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Purification, Saturation and the Exact Law of Large Numbers

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  • Wang, Jianwei
  • Zhang, Yongchao

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.

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File URL: http://mpra.ub.uni-muenchen.de/22119/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 22119.

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Date of creation: Apr 2010
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Handle: RePEc:pra:mprapa:22119

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Keywords: Exact law of large numbers; Fubini extension; Incomplete information; Purification; Saturated probability space;

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  1. Khan, M. Ali & Rath, Kali P., 2009. "On games with incomplete information and the Dvoretsky-Wald-Wolfowitz theorem with countable partitions," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 830-837, December.
  2. Nicholas Yannelis, 2009. "Debreu’s social equilibrium theorem with asymmetric information and a continuum of agents," Economic Theory, Springer, vol. 38(2), pages 419-432, February.
  3. Konrad Podczeck, 2009. "On purification of measure-valued maps," Economic Theory, Springer, vol. 38(2), pages 399-418, February.
  4. Sun, Yeneng, 1998. "A theory of hyperfinite processes: the complete removal of individual uncertainty via exact LLN1," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 419-503, May.
  5. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer, vol. 45(1), pages 1-22, October.
  6. Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
  7. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
  8. Podczeck, Konrad, 2008. "On the convexity and compactness of the integral of a Banach space valued correspondence," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 836-852, July.
  9. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer, vol. 2(3), pages 427-33, July.
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Cited by:
  1. 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.
  2. Michael Greinecker & Konrad Podczeck, 2013. "Purification and Independence," Working Papers 2013-18, Faculty of Economics and Statistics, University of Innsbruck.
  3. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2012. "Large Games with a Bio-Social Typology," Working Papers 035, Ryerson University, Department of Economics.
  4. Yu, Haomiao & Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 0. "Strategic uncertainty and the ex-post Nash property in large games," Theoretical Economics, Econometric Society.
  5. Khan, M. Ali & Zhang, Yongchao, 2014. "On the existence of pure-strategy equilibria in games with private information: A complete characterization," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 197-202.

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