Problem $3(4$ points$)$

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 $C\text{'}$s actions when A sets a tariff and when

it does not, respectively. The game is played simultaneously, and payoffs are written $(U_A,U_B,U_C).$

$3\mathrm{.}1$ What is $C\text{'}$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?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 $).$