  Many three-party correlations, including some that are commonly described as
genuinely tripartite nonlocal, can be simulated by a network of underlying
subsystems that display only bipartite nonsignaling nonlocal behavior. Quantum
mechanics predicts three-party correlations that admit no such simulation,
suggesting there are versions of nonlocality in nature transcending the
phenomenon of bipartite nonsignaling nonlocality. This paper introduces a
rigorous framework for analyzing tripartite correlations that can be simulated
by bipartite-only networks. We confirm that expected properties of so-obtained
correlations, such as no-signaling, indeed hold, and show how to use the
framework to derive Bell-inequality-type constraints on these correlations that
can be robustly violated by tripartite quantum systems. In particular, we use
this framework to rederive a version of one such constraint previously
described in a paper of Chao and Reichardt (arXiv:1706.02008).
