Consider a two$-$player, sequential$-$move game where each player can choose to play right or left. Player $1$ moves first. Player $2$ observes player $1$s actual move and then decides to move right or left. If player $1$ moves right, player $1$ receives $$0$ and player $2$ receives $$25.$ If both players move left, player $1$ receives $$$$5$ and player $2$ receives $$10.$ If player $1$ moves left and player $2$ moves right, player $1$ receives $$20$ and player $2$ receives $$20.($Hint: Before answering the questions below, write the above game in extensive form$).$

a$.$ Find the Nash equilibrium outcomes to this game.

multiple choice $1$

$($$$0,$ $$25)$ and $($$$5,$ $$10)$

$($$$0,$ $$25)$ and $($$$20,$ $$20)$

$($$$20,$ $$20)$ and $($$$5,$ $$10)$

b$.$ Which of the equilibrium outcomes is most reasonable?

multiple choice $2$

$($$$20,$ $$20)$

$($$$0,$ $$25)$

$($$$5,$ $$10)$