Stable cost sharing in production allocation games

Suppose that a group have demands for some good. Each one of them owns a technology to produce the good, with these technologies varying in their effectiveness. We consider technologies exhibiting either increasing return to scale (IRS) or decreasing returns to scale (DRS). In each case, we solve the issue of the efficient allocation of the production between the agents. In the case of IRS, we prove that it is always efficient to centralize the production of the good, whereas efficiency in the case of DRS typically requires to spread the production. We then show that there exist stable cost sharing mechanisms whether we have IRS or DRS. Finally, we characterize a family of stable mechanisms exhibiting no price discrimination (agents are charged the same price for each unit demanded). Under some specific circumstances, our method generates the full core of the problem.