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Purification, saturation and the exact law of large numbers

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  • Jianwei Wang

    ()

  • Yongchao Zhang

    ()

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. Copyright Springer-Verlag 2012

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File URL: http://hdl.handle.net/10.1007/s00199-010-0593-3
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 50 (2012)
Issue (Month): 3 (August)
Pages: 527-545

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Handle: RePEc:spr:joecth:v:50:y:2012:i:3:p:527-545

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Related research

Keywords: Exact law of large numbers; Fubini extension; Incomplete information; Purification; Saturated probability space; C60; C70;

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References

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  1. 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.
  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. Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
  4. 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.
  5. 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.
  6. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer, vol. 45(1), pages 1-22, October.
  7. 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.
  8. Konrad Podczeck, 2009. "On purification of measure-valued maps," Economic Theory, Springer, vol. 38(2), pages 399-418, February.
  9. 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.
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Citations

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Cited by:
  1. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng & Yu, Haomiao, 2013. "Large games with a bio-social typology," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1122-1149.
  2. 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.
  3. 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.
  4. 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.
  5. Michael Greinecker & Konrad Podczeck, 2013. "Purification and Independence," Working Papers 2013-18, Faculty of Economics and Statistics, University of Innsbruck.

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