Play-once DG game Nash-solvability conjecture

Let an $n$-person deterministic graphical game be play-once if every player makes at most one move during a play. The game is Nash-solvable if it has a Nash equilibrium in pure stationary strategies. Play-once Nash-solvability conjecture. Every play-once $n$-person DG game is Nash-solvable. This conjecture is one of the conjectures that remains open in the paper, although the stronger conjunction of being play-once and satisfying CND$(C_0)$ is stated to be sufficient for the existence of a Nash equilibrium.