The study of \(\textsf{SAT}\) and its variants has provided numerous \(\textsf{NP}\) -complete problems, from which most \(\textsf{NP}\) -hardness results were derived. Due to the \(\textsf{NP}\) -hardness of \(\textsf{SAT}\) , adding constraints to either specify a more precise \(\textsf{NP}\) -complete problem or to obtain a tractable one helps better understand the complexity class of several problems. In 1984, Tovey proved that bounded-degree \(\textsf{SAT}\) is also \(\textsf{NP}\) -complete, thereby providing a tool for performing \(\textsf{NP}\) -hardness reductions even with bounded parameters, when the size of the reduction gadget is a function of the variable degree. In this work, we initiate a similar study for \(\textsf{QBF} \) , the quantified version of \(\textsf{SAT}\) . We prove that, like \(\textsf{SAT}\) , the truth value of a maximum degree two quantified formula is polynomial-time computable. However, surprisingly, while the truth value of a 3-regular 3- \(\textsf{SAT}\) formula can be decided in polynomial time, it is \(\textsf{PSPACE}\) -complete for a 3-regular \(\textsf{QBF} \) formula. A direct consequence of these results is that Avoider-Enforcer and Client-Waiter positional games are \(\textsf{PSPACE}\) -complete when restricted to bounded-degree hypergraphs. To complete the study, we also show that Maker-Breaker and Maker-Maker positional games are \(\textsf{PSPACE}\) -complete for bounded-degree hypergraphs.