  We consider the most general correlations that can be obtained by a group of
parties whose causal relations are well-defined, although possibly
probabilistic and dependent on past parties' operations. We show that, for any
fixed number of parties and inputs and outputs for each party, the set of such
correlations forms a convex polytope, whose vertices correspond to
deterministic strategies, and whose (nontrivial) facets define so-called causal
inequalities. We completely characterize the simplest tripartite polytope in
terms of its facet inequalities, propose generalizations of some inequalities
to scenarios with more parties, and show that our tripartite inequalities can
be violated within the process matrix formalism, where quantum mechanics is
locally valid but no global causal structure is assumed.
