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Monte Carlo sampling processes and incentive compatible allocations in large economies
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Hammond, Peter J., Qiao, Lei and Sun, Yeneng (2021) Monte Carlo sampling processes and incentive compatible allocations in large economies. Economic Theory, 71 . pp. 1161-1187. doi:10.1007/s00199-020-01318-5 ISSN 0938-2259.
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Official URL: https://doi.org/10.1007/s00199-020-01318-5
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).
Item Type: | Journal Article | ||||||||
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Subjects: | H Social Sciences > HB Economic Theory | ||||||||
Divisions: | Faculty of Social Sciences > Economics | ||||||||
Library of Congress Subject Headings (LCSH): | Economics, Mathematical, Monte Carlo method, Sampling (Statistics), Hilbert space | ||||||||
Journal or Publication Title: | Economic Theory | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0938-2259 | ||||||||
Official Date: | April 2021 | ||||||||
Dates: |
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Volume: | 71 | ||||||||
Page Range: | pp. 1161-1187 | ||||||||
DOI: | 10.1007/s00199-020-01318-5 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 15 October 2020 | ||||||||
Date of first compliant Open Access: | 30 April 2021 |
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