Conditional exact law of large numbers and asymmetric information economies with aggregate uncertainty

摘要

A stochastic model with a continuum of economic agents often involves shocks at both macro and micro levels. This can be formalized by a continuum of conditionally independent random variables given the macro level shocks. Based on the framework of a Fubini extension, the results on the exact law of large numbers and its converse for a continuum of independent random variables in Sun (J Econ Theory 126:31-69, 2006) are extended to the setting with conditional independence given general macro states. It also follows from Hammond and Sun (Econ Theory 36:303-325,2008) that the conditional independence assumption is generally satisfied. As an illustrative application, it is shown that any ex ante efficient allocation in an asymmetric information economy with general aggregate uncertainty has a (utility) equivalent allocation that is incentive compatible, which generalizes the corresponding results in Sun and Yannelis (Games Econ Behav 61:131-155, 2007) to the case with infinitely many states.