A non-empty coalition S is said to block an allocation x if there exist x’i E Xi, i E S, and y^S E Y^S such that
(1) x’i > xi for all i E S
(2) Σx’i = Σ ei + y^S
i E S
Then the core is defined as the set of feasible allocations which are blocked by no coalition.
Since, in the socialism economies there are no coalition, one may think that the feasible allocations for such economies are in the core. But such allocations are imposed and therefore may no be voluntary and then the exchange can´t be unfettered so i don´t think that a socialism economy is in the core.