Question $4.$ Zeynep and Mehmet will eventually play the following game.

$\backslash$table$[[,,$Mehmet$],[$Zeynep$,,L,],[,U,3,1,0,0],[,D,0,3,1,3],[,,,]]$

In a preliminary stage, Zeynep has already asked Mehmet to allow her to move first and proposed to pay him $1$ unit of her own payoff in exchange. So Mehmet has to options:

If he accepts Zeynep's offer: they will play the sequential move version of the above game in which Zeynep moves first. Mehmet will receive $1$ unit of utility more, and Zeynep will receive $1$ unit of utility less $($in any outcome of the game$)$ compared to the payoffs given in the bimatrix.

$2$

If he rejects Zeynep's offer: they will play the simultaneous move game.

a$.$ Represent this strategic interaction in a game tree.

b$.$ How many information sets does each player have?

c$.$ Characterize the set of pure strategies for both players.

d$.$ Present this game as a normal$-$form game, and characterize the set of pure strategy Nash equilibria.