Game tree for a $2$ player sequential game. If P$1$ and P$2$ both pick up$,$ P$1$ gets $$100$ and P$2$ gets $$0.$ If P$1$ picks up and P$2$ picks down, P$1$ gets $$52$ and P$2$ gets $$2.$ If P$1$ picks down and P$2$ picks up$,$ P$1$ gets $$25$ and P$2$ gets $$29.$ If both pick down, P$1$ gets $$50$ and P$2$ gets $$50$ In the game above, what is$/$are the sub$-$game perfect Nash equilibrium? $($up$,$up$)($up$,$down$)($down$,$ up$)($down$,$ down$)$ No equilibrium exists