A Consistent Allocation Rule: Non-emptiness, Reductions, Domination and Axiomatization

Since an extended core violates related properties of consistency, this paper proposes the concept of pseudo core. By focusing on the agents and the operational levels simultaneously, an extended reduction is also introduced to axiomatize the pseudo core. Furthermore, this paper adopts the duality results of linear programming theory to determine the non-emptiness of the pseudo core. By investigating the domination among payoff vectors, this article also proposes the dominance core and related coincidences between the pseudo core and the dominance core.