Consistent Subsolutions of the Least Core

The least core, a well-known solution concept in TU games setting, satisfies many properties used in axiomatizations of TU game solutions: it is efficient, anonymous, covariant, possesses shift-invariance, and max-invariance. However, it is not consistent thought the prenucleolus, that is consistent, is contained in it. Therefore, the least core may contain other consistent subsolutions. Since the union of consistent in the sense of Davis–Maschler solutions is also consistent, there should exist the unique maximal under inclusion consistent subsolution of the least core. In the paper we present and characterize this solution.