Answer Happy

Two countries, A and B, play a game of tariffs. If they impose
tariff on each other, then both countries get a payoff of $1
billion. If neither imposes tariff, then both countries get a
payoff of $4 billion. If one of them imposes tariff and the other
does not, then the country who imposes tariffs gets $5 billion and
the other one gets zero.
(a) Write down the payoff matrix for the two countries.
Characterize the Nash equilibrium outcome of this game.
(b) Now suppose the two countries play this game repeatedly for
four periods. Before playing, they reach mutual agreements as
follows: In period 1, neither county imposes tariff. In
period 2, country A has the option of imposing tariff or not. If
country A imposes tariff, country B will retaliate by imposing
tariff in period 3 and 4. If country A does not impose tariff,
country B will never change its non-tariff policy. There is a
discount factor 𝛿 ∈ (0,1) that works as follows. If the country’s
payoff in the four periods is 𝑎1, 𝑎2, 𝑎3 and 𝑎4, respectively, then
it makes decisions by looking at the discounted payoff: 𝜋 = 𝑎1 +
𝛿𝑎2 + 𝛿 2𝑎3 + 𝛿 3𝑎4
i) Suppose country A’s decision in period 2 can never be
reversed in the subsequent periods. Under what condition of 𝛿, will
the country A decide not to impose tariff in period 2? only
need the condition(s) that 𝛿 should satisfy. No need to solve
explicitly for the range of 𝛿