Builder-Blocker game complexity

Determine the computational complexity of the decision versions of the Builder and Blocker general position games.

Background

The Builder/Blocker games build a maximal general-position set under opposing objectives. The survey states that the decision complexity is completely unknown and records the conjecture that both game variants are PSPACE-complete.

References

The complexity of the decision version of the Builder/Blocker game is completely unknown, but gives the following conjecture.

— The General Position Problem: A Survey  (2501.19385 - V. et al., 31 Jan 2025) in Section 7, subsection “Games on graphs,” subsection “Complexity of games”