Infinite dimensional mixed economies with asymmetric information

In this paper, we study asymmetric information economies consisting of both non-negligible and negligible agents and having ordered Banach spaces as their commodity spaces. In answering a question of Herv'{e}s-Beloso and Moreno-Garc'{i}a, we establish a characterization of Walrasian expectations allocations by the veto power of the grand coalition. It is also shown that when an economy contains only negligible agents a Vind’s type theorem on the private core with the exact feasibility can be restored. This solves a problem of Pesce.