  We define a family of pseudo-telepathy games using graph states that extends
the Mermin games. This family also contains a game used to define a quantum
probability distribution that cannot be simulated by any number of PR boxes. We
extend this result proving that the probability distribution obtained by the
Paley graph state on 13 vertices cannot be simulated by any number of 4-partite
non local boxes and that the Paley graph states on more than $k^{2}2^{2k-2}$
vertices provides a probability distribution that cannot be simulated by
k-partite nonlocal boxes
