Consider a tariff$-$setting game between three countries, A$,$ B$,$ and C$.$ These countries are different sizes, and tariffs may have terms$-$of$-$trade effects $($and deadweight losses$).$ The left and right payoff matrices below indicate payoffs from combinations of B and C$$s actions when A sets a tariff and when it does not, respectively. The game is played simultaneously, and payoffs are written $($UA$,$UB$,$UC$).$

$3\mathrm{.}1$ What is C$$s best response if A plays $$No Tariff$$ and B plays $$Tariff$?1$ Tariff

$2$ No Tariff

$3\mathrm{.}2$ How many Nash equilibria does this game have?

For $3\mathrm{.}3,$ suppose that before the game begins, B and C present A an offer: $$if you do not use a tariff, we will each give you $5$ from whatever payoff we get.$$

$3\mathrm{.}3$ What payoff does A end up getting in the Nash equilibrium?

For $3\mathrm{.}4,$ suppose that before the game begins, B and C enter an international agreement to

split their payoffs evenly, regardless of the outcome.

$3\mathrm{.}4$ What payoff does A end up getting in the Nash equilibrium?