We provide several different generalizations of Debreu’s social equilibrium theorem by allowing for asymmetric information and a continuum of agents. The results not only extend the ones in Kim and Yannelis (J Econ Theory 77:330–353, 1977), Yannelis and Rustichini (Stud Econ Theory 2:23–48, 1991), but also new theorems are obtained which allow for a convexifying effect on aggregation (non-concavity assumption on the utility functions) and non-convex strategy sets (pure strategies). This is achieved by imposing the assumption of “many more agents than strategies” (Rustichini and Yannelis in Stud Econ Theory 1:249–265, 1991; Tourky and Yannelis in J Econ Theory 101:189–221, 2001; Podczeck in Econ Theory 22:699–725, 2003).
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机译：通过考虑信息不对称和主体的连续性，我们提供了德布鲁社会均衡定理的几种不同概括。结果不仅扩展了Kim和Yannelis（J Econ Theory 77：330-353，1977），Yannelis和Rustichini（Stud Econ Theory 2：23-48，1991）中的定理，而且获得了新的定理，使得对聚合（效用函数的非凹假设）和非凸策略集（纯策略）产生凸化作用。这是通过强加“行为主体多于策略”的假设来实现的（Rustichini和Yannelis，《梭子经济理论》 1：249–265，1991； Tourky和Yannelis，《经济学理论》 101：189–221，2001； Podczeck的《经济学理论》）。 22：699–725，2003年）。
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