Matching with ownership

We consider a hybrid model at the intersection of standard two-sided matching market as proposed by Gale and Shapley (1962) housing Scarf (1974). Two sets agents have to be matched in pairs common set objects. Agents one type preferences that depend on not only object they are but also agent other this object. The crucial difference lies fact side is interpreted an has no intrinsic over it. introduce natural definition ownership objects determines which owns he to. Ownership restricts objections who owners defines notion stability. two structures show stable matchings exist both structures. first structure, i.e., one-side ownership, always gives same side. Even if structure shares similarities with classical framework, we following important difference: Pareto-efficient can disjoints, implying core empty. propose subdomains preferences, lexicographic couple where one-sided second joint any reallocation must jointly agreed upon initially assigned them. As discussed Morrill (2010), equivalent matchings, discuss possible algorithms used check Pareto efficiency. Finally, general ownerships ones guarantee existence matchings. To further investigate link literature, initial allocation define respect allocation. contrast setting, However, there exists blocked coalition size two. In settings, pairwise stability minimal requirement ensure.