$(12$ points$)$ Imagine that two players play the following game in each stage repeatedly and forever. Also, assume that they share the same discount factor $$ of future payoffs.

$\backslash$table$[[$Player $1$

B$,$Player $2],[$T$,$L$,$R$],[5,0,1,2],[3,4,0,7]]$

$($a$)(1$ point$)$ What is the pure$-$strategy Nash equilibrium of the stage game?

$($b$)(1$ point$)$ For the Nash equilibrium you find in part $($a$),$ is it Pareto efficient?If not, find an outcome of the above game that is more Pareto efficient than the Nash equilibrium.

$($c$)(10$ points$)$ Would you expect the Grim Trigger strategy to be a sufficient punishment mechanism for the two players to achieve the Pareto efficient outcome in each stage? Justify your conclusion.