  Quantum correlations are expected to respect all the conditions required for
them to be good measures of quantumness in the bipartite scenario. In a
multipartite setting, sharing entanglement between several parties is
restricted by the monogamy of entanglement. We take over the concept of
monogamy to an information-theoretic quantum correlation measure, and find that
it violates monogamy in general. Using the notion of interaction information,
we identify necessary and sufficient conditions for the measure to obey
monogamy, for arbitrary pure and mixed quantum states. We show that while
three-qubit generalized Greenberger-Horne-Zeilinger states follow monogamy,
generalized W states do not.
