Generalized coalitions and bargaining sets

We introduce new notions of bargaining set for mixed economies which rest on the idea of generalized coalitions (Aubin, 1979) to define objections and counter-objections. We show that the bargaining set defined through generalized coalitions coincides with competitive allocations under assumptions which are weak and natural in the mixed market literature. As a further result, we identify some additional properties that a generalized coalition must satisfy to object an allocation.