We study the problem of deciding the winner of reachability switching games for zero-, one-, and two-player variants. Switching games provide a deterministic analogue of stochastic games. We show that the zero-player case is NL-hard, the one-player case is NP-complete, and that the two-player case is PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness for a succinctly-represented model that maintains the upper bound of NP $\cap$ coNP. For the one- and two-player cases, our results hold in both the natural, explicit model and succinctly-represented model. Our results show that the switching variant of a game is harder in complexity-theoretic terms than the corresponding stochastic version.

@article{paperbot1318,
  title = {Reachability Switching Games},
  author = {John Fearnley and Martin Gairing and Matthias Mnich and Rahul Savani},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 17, Issue 2},
  year = {2021},
  doi = {10.23638/lmcs-17(2:10)2021}
}