Core is manipulable via segmentation

Any allocation rule that picks only core allocations is manipulable via segmentation. That is, there exists an economy with a coalition of agents such that, once this coalition splits momentarily from the rest of the economy and institutes the allocation rule within itself, no matter which individually rational sub-allocation the complementary coalition picks, when we paste all the agents back together at their new endowments and apply the allocation rule to this “collage” economy, each member of the former coalition will be strictly better off than under direct application of the allocation rule to the original economy.