Before revision: In discrete exchange economies with possibly redundant and joint ownership, the conventional strong core may be empty , while the weak core may include unintuitive outcomes. We propose new core notions in the conventional flavor by regarding endowments as rights to consume or trade with others. Our key idea is to identify self-enforcing coalitions and to redistribute their redundant property rights. Our first notion lies between the strong core and the weak core and is independent of Balbuzanov and Kotowski's (2019) exclusion core .
After revision: In discrete exchange economies with possibly redundant and joint ownership, the conventional strong core may be empty . This motivates Balbuzanov and Kotowski (2019) to interpret endowments as exclusion rights and propose a new concept called exclusion core. Our contribution is twofold. First, we propose a rectification of the core to solve its problem under complex endowments. Second, we propose a refinement of Balbuzanov and Kotowski's (2019) exclusion core .