  This paper investigates the ex-post core and its relationships to the fine
core and the set of rational expectations equilibrium allocations in an
oligopolistic economy with asymmetric information, in which the set of agents
consists of some large agents and a continuum of small agents and the space of
states of nature is a general probability space. We show that under appropriate
assumptions, the ex-post core is not empty and contains the set of rational
expectations equilibrium allocations. We provide an example of a pure exchange
continuum economy with asymmetric information and infinitely many states of
nature, in which the ex-post core does not coincide with the set of rational
expectations equilibrium allocations. We also show that when our economic model
contains either no large agents or at least two large agents with the same
characteristics, the fine core is contained in the ex-post core.
