Debreu's social equilibrium theorem with asymmetric information and a continuum of agents

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).