On the core of an economy with arbitrary consumption sets and asymmetric information

We study core allocations in a two-period asymmetric information mixed economy, where the consumption sets are arbitrary subsets of an ordered Banach space, and the feasibility is defined as exact. We prove that (i) the strong blocking by a generalized coalition leads to a weak blocking by some ordinary coalition, implying the equivalence between the Aubin core and the core of an economy with only negligible agents; and (ii) the core can be characterized in terms of the size (and diameter) of the blocking coalitions in an economy with only negligible agents as well as both negligible and non-negligible agents.