Our study explores multipartite nonlocality by extending $2$-player nonlocal games to multiplayer games, where the players are positioned across the vertices of a graph. We characterize when $2$-player games cannot violate Bell nonlocality on graphs with more than $2$ vertices. Using similar techniques, we show the CHSH game only exhibits nonlocality in two distributed scenarios: the original 2-player game and the 4-player game on the path graph. In contrast, several other well-studied games have no such violations on larger graphs. Lastly, we provide a $2$-player game that exhibits nonlocality on infinitely many graphs.
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Cui et al. (2024) studied this question.
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