  Strategy Logic (SL) is a very expressive logic for specifying and verifying
properties of multi-agent systems: in SL, one can quantify over strategies,
assign them to agents, and express properties of the resulting plays. Such a
powerful framework has two drawbacks: first, model checking SL has
non-elementary complexity; second, the exact semantics of SL is rather
intricate, and may not correspond to what is expected. In this paper, we focus
on strategy dependences in SL, by tracking how existentially-quantified
strategies in a formula may (or may not) depend on other strategies selected in
the formula. We study different kinds of dependences, refining the approach of
[Mogavero et al., Reasoning about strategies: On the model-checking problem,
2014], and prove that they give rise to different satisfaction relations. In
the setting where strategies may only depend on what they have observed, we
identify a large fragment of SL for which we prove model checking can be
performed in 2EXPTIME.
