Consistency and the exclusion core in object allocation with co-ownership

We employ the consistency principle to evaluate core concepts in an indivisible object allocation model with intricate co-ownership. In this environment, the strong core is consistent but may be empty, the weak core is nonempty but neither consistent nor Pareto efficient, and the exclusion core introduced by Balbuzanov and Kotowski (2019), although nonempty and Pareto efficient, fails consistency. We introduce the concept of refined exclusion core that preserves the exclusion-rights approach while restoring consistency. The refined exclusion core eliminates unreasonable allocations admitted by the exclusion core and delivers sharper predictions than existing alternatives.