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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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
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:	Date Event April 2021 Published 23 October 2020 Available 6 October 2020 Accepted
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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