Ekici’s reclaim-proof allocations revisited

We revisit the concept of reclaim-proof allocations proposed by Ekici (2013) for house allocation problems with existing tenants. As a concept of core, the definition of reclaim-proof allocations assumes that when a coalition blocks an allocation, an agent in the coalition is allowed to bring her allocated object into the coalition, even when it is privately owned by an outsider. We propose a new notion of core called the effectual core by restoring the feasibility of coalitional blocking in Ekici’s definition. Our main result shows that the effectual core, while by definition weaker than reclaim-proofness, is actually equivalent to it. Together with Ekici’s results, it is then immediate that an allocation is in the effectual core if and only if it is produced by the You request my house-I get your turn (YRMH-IGYT) mechanism (Abdulkadiroğlu and Sönmez, 1999) and if and only if it is a competitive allocation.