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We present a multipartite nonlocal game in which each player must guess theinput received by his neighbour. We show that quantum correlations do notperform better than classical ones at this game, for any prior distribution ofthe inputs. There exist, however, input distributions for which generalno-signalling correlations can outperform classical and quantum correlations.Some of the Bell inequalities associated to our construction correspond tofacets of the local polytope. Thus our multipartite game identifies parts ofthe boundary between quantum and post-quantum correlations of maximaldimension. These results suggest that quantum correlations might obey ageneralization of the usual no-signalling conditions in a multipartite setting.

Guess your neighbour's input: a multipartite non-local game with no quantum advantage