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We define a family of pseudo-telepathy games using graph states that extendsthe Mermin games. This family also contains a game used to define a quantumprobability distribution that cannot be simulated by any number of PR boxes. Weextend this result proving that the probability distribution obtained by thePaley graph state on 13 vertices cannot be simulated by any number of 4-partitenon 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 byk-partite nonlocal boxes

Pseudo-telepathy games and genuine NS k-way nonlocality using graph states