A cost sharing example in which subsidies are necessary for stability

Suppose that agents, who have demands for some goods, cooperate to produce their joint demands. If the technology for the production of these goods improves as the set of cooperating agents grows, we have a justification for subsidies when an agent has such an efficient technology that he is able to generate savings for the group. While it was known that there may exist some stable allocations with subsidies (i.e, negatives cost shares), our...