This note provides a generalization of the equal allocation of nonseparable costs (EANSC) on multi-choice games. Also, we extend to the multi-choice games case the complement reduced game and characterize the extended EANSC by means of related property of consistency.

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...