Hierarchy of multipartite nonlocality in the nonsignaling scenario

We propose a hierarchy of Bell-type inequalities for arbitrary $n$-partite systems that identifies the different degrees of nonlocality ranging from standard to genuine multipartite nonlocality. After introducing the definition of nonsignaling $m$ locality, we show that the observed joint probabilities in any nonsignaling $m$-local realistic models should satisfy the $(m\ensuremath{-}1)\mathrm{th}$ Bell-type inequality. When $m=2$, the corresponding inequality reduces to the one shown earlier [Q. Chen et al., Phys. Rev. Lett. 112, 140404 (2014)] whose violation indicates genuine multipartite nonlocality, and when $m=n$, the corresponding inequality is just Hardy's inequality whose violation indicates standard multipartite nonlocality. Furthermore, several examples are provided to demonstrate their hierarchy of multipartite nonlocality.