Problem $2.$ Consider the following zero$-$sum game

$\backslash$table$[[,$W$,$X$,$Y$,$Z$],[$A$,7,-12,0,1],[$B$,3,-5,-2,-3],[$C$,5,-4,4,-10],[$D$,4,-8,-9,0]]$

a$)(7$ points$)$ Find the maximin and minimax and state whether the game has a Nash equilibrium. Please show your work on the payoff matrix above.

Maximin $=$

Minimax $=$

Nash equilibria?

b$)(3$ points$)$ Suppose Player $1$ chooses strategy C and Player $2$ chooses strategy X $.$

State the player who can unilaterally change strategy to improve their payoff and the new strategy giving a better payoff for this player.