PSPACE-completeness conjecture for Fast-Strategy on bipartite graphs

Let $G$ be a bipartite graph, and let $t$ denote the number of guards in the eternal domination game. The decision problem $\textsc{Fast-Strategy}$ asks whether the guards have a strategy satisfying the fast-winning condition on $G$. Fast-Strategy conjecture. The problem $\textsc{Fast-Strategy}$ is PSPACE-complete on bipartite graphs. This conjecture is motivated by the PSPACE-hardness results for related graph classes and by the frequent dichotomy between polynomial-time solvability and PSPACE-hardness in game problems; the completeness of Fast-Strategy on bipartite graphs remains open.