Stable cost sharing in production allocation games

Suppose that a group of agents have demands for some good. Every agent owns a technology which allows them to produce the good, with these technologies varying in their effectiveness. If all technologies exhibit increasing returns to scale (IRS) then it is always efficient to centralize production of the good, whereas efficiency in the case of decreasing returns to scale (DRS) typically requires to spread production. We search for stable cost allocations while differentiating allocations with homogeneous prices, in which all units produced are traded at the same price, from allocations with heterogeneous prices. For the respective cases of IRS or DRS, it is shown that there always exist stable cost sharing rules with homogeneous prices. Finally, in the general framework (under which there may exist no stable allocation at all) we provide a sufficient condition for the existence of stable allocations with homogeneous prices. This condition is shown to be both necessary and sufficient in problems with unitary demands.