Monte Carlo sampling processes and incentive compatible allocations in large economies

Peter Hammond, Lei Qiao () and Yeneng Sun ()
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Lei Qiao: Shanghai University of Finance and Economics
Yeneng Sun: National University of Singapore

Economic Theory, 2021, vol. 71, issue 3, No 11, 1187 pages

Abstract: 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 ).

Keywords: Law of large numbers; Monte Carlo sampling process; One-way Fubini property; Hilbert space; Incentive compatibility; Asymmetric information; Pareto efficiency (search for similar items in EconPapers)
JEL-codes: C65 D51 D61 D82 (search for similar items in EconPapers)
Date: 2021
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Related works:
Working Paper: Monte Carlo Sampling Processes and Incentive Compatible Allocations in Large Economies (2020)
Working Paper: Monte Carlo Sampling Processes and Incentive Compatible Allocations in Large Economies (2019)
Working Paper: Monte Carlo Sampling Processes and Incentive Compatible Allocations in Large Economies (2019)
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DOI: 10.1007/s00199-020-01318-5

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