$2\mathrm{.}2$ Background: Game Theory

Problem $2.$ Consider the following game with two players who choose between strategy A and strategy $B$ :

$\backslash$table$[[,,$Player Y$],[,269$ hats,$A$ B$],[8\mathrm{.}8,$A$,30,6,(20.7],[(3),$Player X $B,(14)10,(33)11]]$

$($a$)$ Indicate all of Player X$\text{'}$s best responses on the matrix by circling them. Does Player X have a dominant strategy?

$($b$)$ Indicate all of Player Y$\text{'}$s best responses on the matrix by circling them. Does Player Y have a dominant strategy?

c$)$ What is the Nash equilibrium?

$32$