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

Author

Listed:
  • Lei Qiao

    () (National University of Singapore)

  • Yeneng Sun

    () (National University of Singapore)

  • Zhixiang Zhang

    () (Central University of Finance and Economics)

Abstract

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.

Suggested Citation

  • Lei Qiao & Yeneng Sun & Zhixiang Zhang, 2016. "Conditional exact law of large numbers and asymmetric information economies with aggregate uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 43-64, June.
  • 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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    References listed on IDEAS

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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.
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    Cited by:

    1. repec:spr:joecth:v:64:y:2017:i:1:d:10.1007_s00199-016-0993-0 is not listed on IDEAS
    2. Marcel Nutz, 2016. "A Mean Field Game of Optimal Stopping," Papers 1605.09112, arXiv.org, revised Nov 2017.
    3. Felix J. Bierbrauer & Martin F. Hellwig, 2015. "Public-Good Provision in Large Economies," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_12, Max Planck Institute for Research on Collective Goods.

    More about this item

    Keywords

    Conditional exact law of large numbers; Fubini extension; Conditional independence; Asymmetric information; Ex ante efficiency; Incentive compatibility;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • E00 - Macroeconomics and Monetary Economics - - General - - - General

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