Monogamy of multipartite Bell inequality violations

We show that the complementarity relation between dichotomic observables leads to the monogamy of Bell inequality violations. We introduce a simple condition for the squares of expectation values of complementary observables that is satisfied by all physical states. This condition is used to study multi-qubit correlation inequalities involving two settings per observer. In contrast with the two-qubit case a rich structure of possible violation patterns is shown to exist in the multipartite scenario.