$1.$ Consider the following $\backslash (2\backslash$times $2\backslash )$ payoff matrix.

Player $2$

a$)$ If Player $1$ plays strategy B$,$ and Player $2$ plays strategy A$,$ then what is the respective payoffs for each player? $[1$ mark$]$

b$)$ Does Player $1$ or Player $2$ have a Dominant Strategy? If so$,$ what is$/$are they. No need to show your work. $[2$ mark$]$

c$)$ Does this game have a Nash Equilibrium? If so$,$ what is$/$are they? No need to show your work. $[1$ mark$]$

$2.$ Consider the following $\backslash (2\backslash$times $2\backslash )$ payoff matrix.

Player $2$

a$)$ Find Player $1$ and Player $2\text{'}$s dominant strategies $($if they have one$).$ Also determine$/$state any Nash Equilibrium. $[3$ marks$]$

b$)$ Construct a new payoff matrix $($by filling in the below$)$ that has the same dominant strategies and Nash Equilibrium as the game above. You can not use any of the numbers used in the game above. $[2$ marks$]$