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Monte Carlo sampling processes and incentive compatible allocations in large economies

Author

Listed:
  • Peter J. Hammond

    (University of Warwick)

  • Lei Qiao

    (Shanghai University of Finance and Economics)

  • Yeneng Sun

    (National University of Singapore)

Abstract

Monte Carlo simulation is used in Hammond and Sun (Econ Theory 36:303–325, 2008. https://doi.org/10.1007/s00199-007-0279-7 ) to characterize a standard stochastic framework involving a continuum of random variables that are conditionally independent given macro shocks. This paper presents some general properties of such Monte Carlo sampling processes, including their one-way Fubini extension and regular conditional independence. In addition to the almost sure convergence of Monte Carlo simulation considered in Hammond and Sun (2008), here we also consider norm convergence when the random variables are square integrable. This leads to a necessary and sufficient condition for the classical law of large numbers to hold in a general Hilbert space. Applying this analysis to large economies with asymmetric information shows that the conflict between incentive compatibility and Pareto efficiency is resolved asymptotically for almost all sampling economies, following some similar results in McLean and Postlewaite (Econometrica 70:2421–2453, 2002) and Sun and Yannelis (J Econ Theory 134:175–194, 2007. https://doi.org/10.1016/j.jet.2006.03.001 ).

Suggested Citation

  • Peter J. Hammond & Lei Qiao & Yeneng Sun, 2021. "Monte Carlo sampling processes and incentive compatible allocations in large economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1161-1187, April.
    • Handle: RePEc:spr:joecth:v:71:y:2021:i:3:d:10.1007_s00199-020-01318-5
    DOI: 10.1007/s00199-020-01318-5
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    References listed on IDEAS

    as
    1. Yeneng Sun & Nicholas Yannelis, 2008. "Ex ante efficiency implies incentive compatibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(1), pages 35-55, July.
    2. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    3. Peter Hammond & Yeneng Sun, 2008. "Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(2), pages 303-325, August.
    4. 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.
    5. 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.
    6. Richard McLean & Andrew Postlewaite, 2002. "Informational Size and Incentive Compatibility," Econometrica, Econometric Society, vol. 70(6), pages 2421-2453, November.
    7. 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.
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    More about this item

    Keywords

    Law of large numbers; Monte Carlo sampling process; One-way Fubini property; Hilbert space; Incentive compatibility; Asymmetric information; Pareto efficiency;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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