Consider the game where Player $1$ plays A$,$ B$,$ C$,$ D; and Player $2$ plays R$,$ Q$,$ S$,$ T with the following

payoffmatrix:

R Q S T

A $2,21,11,11,1$

B $1,14,31,11,1$

C $1,11,13,41,1$

D $1,11,11,15,5$

With reference to the matrix above, answer the following questions:

$1.$ Identify with justification, if any, the pairs that are in Nash equilibrium.

$2.$ State whether any outcomes are Pareto optimal. Justify your answer.

$3.$ Identify with justification, if any, the pairs that maximizes the social welfare.