Solution to exercise

Find the countries' best response functions. To find the best response function of country 1, solve
max_t_₁[t₁(t₁ t₂ 2)].
We find b₁(t₂) = (1/2)(t₂ + 2). Similarly the best response function of country 2 is b₂(t₁) = (1/2)(t₁ + 8).
Solve for the Nash equilibria. A Nash equilibrium is a pair (t₁*,t₂*) such that t₁* = b₁(t₂*) and t₂* = b₂(t₁*). These two equations have a unique solution, (t₁, t₂) = (4,6).

We conclude that the game has a unique Nash equilibrium, (t₁*, t₂*) = (4,6).