Question $4(2$ points$)$

In the game with the payoff matrix

above, agents A and B decide independently to contribute $0,1$ or $2$ units of a good into a common pool. Choose each correct statement from the following. The outcome that B most prefers occurs if

$1)\backslash ($ A $\backslash )$ contributes $0$ and $\backslash ($ B $\backslash )$ contributes $2.$

$2)$ both agents contribute $2.$

$3)\backslash ($ A $\backslash )$ contributes $2$ and $\backslash ($ B $\backslash )$ contributes $0.$

$4)$ both agents contribute $0.$

$5)$ both agents contribute $1.$

Question $5(2$ points$)$

Choose each correct statement about the game of problem $4.$

$1)$ Each agent has a dominant strategy of contributing $0.$

$2)$ There is a unique Nash equilibrium in which each agent contributes $0.$

$3)$ There are two Nash equilibria and in each, exactly one agent contributes.

$4)$ One outcome $($represented by a single square$)$ is Pareto superior to every Nash equilibrium.