The Hospitals / Residents problem with Free Pairs

In the classical Hospitals/Residents problem, a stable matching M is sought which ensures that no blocking pair can exist in which a resident r and hospital h can improve relative to M by becoming assigned to each other. Such a situation is undesirable as it could naturally lead to r and h forming a private arrangement outside of the matching. This however assumes that a blocking pair that exists in theory would invariably lead to a matching being undermined in practice. However such a situation need not arise if the lack of social ties between agents prevents an awareness of certain blocking pairs in practice. Relaxing the stability definition to take such a scenario into account can yield larger stable