$13.$ Consider the following game.

a$.$ Find all subgame perfect Nash equilibria $($you can indicate the SPNE by writing arrows in the tree$).$

b$.$ Find all $($pure strategy$)$ Nash equilibria of this game.

c$.$ Now consider the following game. Please note that two of the payoffs are now variables x and y$\mathrm{.}1$

d$.$ Circle all values of x and y in the table below for which there is more than one subgame perfect Nash equilibrium. For example, if there is more than one subgame perfect Nash equilibrium when x $=1$ and y $=1,$ then circle x$=1$ y$=1.$ Please explain your work.

e$.$ Here is the game again.

f$.$ Circle all values of x and y in the table below for which there are exactly two $($pure

strategy$)$ Nash equilibria. For example, if there are exactly two Nash equilibria when x $=3$ and y $=2,$ then circle x$=3$ y$=2.$ Please explain your work.