# One Sided Matching Problems with Capacity

Présentation de Ipek Ozkal Sanver (Istanbul Bilgi University)

Présentation de Ipek Ozkal Sanver (Istanbul Bilgi University)
En collaboration avec Duygu Nizamogullari (Piri Reis University)

Abstract : Classical roommate problems define individual rationality by conceiving remaining single as the "outside option". This conception implicitly assumes that there is no capacity constraint, i.e., the number of individuals does not exceed the number of the rooms. However, there are many instances when this is not the case. We introduce roommate problem with capacity constraint where the "outside option" is "having no room". In this general framework with capacity, we show that the wellknown equivalence result between core and set of stable matching does no more hold. Indeed, the core equals the set of matchings which are Pareto optimal and stable. We also consider a restricted model where the capacity constraint is not binding, but there is the option "having no room". The characterization of the core under this framework is our ongoing interest of research.