Monte Carlo Sampling Processes and Incentive Compatible Allocations in Large Economies

Peter Hammond, Lei Qiao and Yeneng Sun
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Lei Qiao: School of Economics, Shanghai University of Finance and Economics
Yeneng Sun: Departments of Economics and Mathematics, National University of Singapore

CRETA Online Discussion Paper Series from Centre for Research in Economic Theory and its Applications CRETA

Abstract: Monte Carlo simulation is used in Hammond and Sun (2008) 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 su cient 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 con ict between incentive compatibility and Pareto efficiency is resolved asymptotically for almost all sampling economies, corresponding to some results in McLean and Postlewaite (2002) and Sun and Yannelis (2007).

Keywords: Law of large numbers; Monte Carlo sampling process; one-way Fubini property; Hilbert space; incentive compatibility; asymmetric information; Pareto efficiency JEL Codes: C65; D51; D61; D82 (search for similar items in EconPapers)
Date: 2020
New Economics Papers: this item is included in nep-des, nep-ore and nep-sea
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https://warwick.ac.uk/fac/soc/economics/research/c ... _-_peter_hammond.pdf

Related works:
Journal Article: Monte Carlo sampling processes and incentive compatible allocations in large economies (2021)
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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