  We present a multipartite nonlocal game in which each player must guess the
input received by his neighbour. We show that quantum correlations do not
perform better than classical ones at this game, for any prior distribution of
the inputs. There exist, however, input distributions for which general
no-signalling correlations can outperform classical and quantum correlations.
Some of the Bell inequalities associated to our construction correspond to
facets of the local polytope. Thus our multipartite game identifies parts of
the boundary between quantum and post-quantum correlations of maximal
dimension. These results suggest that quantum correlations might obey a
generalization of the usual no-signalling conditions in a multipartite setting.
