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Conditional exact law of large numbers and asymmetric information economies with aggregate uncertainty

Listed author(s):
  • Lei Qiao

    ()

    (National University of Singapore)

  • Yeneng Sun

    ()

    (National University of Singapore)

  • Zhixiang Zhang

    ()

    (Central University of Finance and Economics)

Abstract A stochastic model with a continuum of economic agents often involves shocks at both macro and micro levels. This can be formalized by a continuum of conditionally independent random variables given the macro level shocks. Based on the framework of a Fubini extension, the results on the exact law of large numbers and its converse for a continuum of independent random variables in Sun (J Econ Theory 126:31–69, 2006) are extended to the setting with conditional independence given general macro states. It also follows from Hammond and Sun (Econ Theory 36:303–325, 2008) that the conditional independence assumption is generally satisfied. As an illustrative application, it is shown that any ex ante efficient allocation in an asymmetric information economy with general aggregate uncertainty has a (utility) equivalent allocation that is incentive compatible, which generalizes the corresponding results in Sun and Yannelis (Games Econ Behav 61:131–155, 2007) to the case with infinitely many states.

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File URL: http://link.springer.com/10.1007/s00199-014-0855-6
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Article provided by Springer & Society for the Advancement of Economic Theory (SAET) in its journal Economic Theory.

Volume (Year): 62 (2016)
Issue (Month): 1 (June)
Pages: 43-64

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Handle: RePEc:spr:joecth:v:62:y:2016:i:1:d:10.1007_s00199-014-0855-6
DOI: 10.1007/s00199-014-0855-6
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  1. Haomiao Yu, 2014. "Rationalizability in large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 457-479, February.
  2. 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.
  3. Jianwei Wang & Yongchao Zhang, 2012. "Purification, saturation and the exact law of large numbers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 527-545, August.
  4. Peter J. Hammond & Yeneng Sun, 2003. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the symmetric case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 743-766, March.
  5. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 1-22, October.
  6. 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.
  7. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
  8. McLean, Richard & Postlewaite, Andrew, 2005. "Core convergence with asymmetric information," Games and Economic Behavior, Elsevier, vol. 50(1), pages 58-78, January.
  9. Sun, Yeneng & Zhang, Yongchao, 2009. "Individual risk and Lebesgue extension without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 144(1), pages 432-443, January.
  10. McLean, Richard P. & Postlewaite, Andrew, 2003. "Informational size, incentive compatibility, and the core of a game with incomplete information," Games and Economic Behavior, Elsevier, vol. 45(1), pages 222-241, October.
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