Two large countries, A and B, are trading partners. They have to simultaneously decide their op- timal import tariff levels (a tax on imports from the other country). Country A's gains from trade are IIA=18+6-ta6 tB-tA tB-A where t is Country A's tariff level and to is Country B's tariff level. Country B's gains from trade are symmetric: IIB = 18+6 t 6 t - t t t. Maximizing Country A's gains from trade you can see that A's best response function to the tariff level picked by Country B is ta=3-0.5-tB (B's problem is symmetric, therefore we know that B's best response function is t = 3 - 0.5-ta). The only Nash Equilibrium of that game was (t, tB) = (2, 2), while zero tariffs maximized the sum of the gains of trade. (a) Suppose this game is repeated over ten periods. What is the equilibrium path associated to the SPNE of this sequential game? (b) Suppose this game is repeated indefinitely and that both countries have the same discount factor 80.5. Find out if grim-trigger strategies can sustain cooperation at the zero-tariff level. (c) Show that a 1-period temporary reversion to the Nash equilibrium punishment won't be enough to sustain cooperation at the zero-tariff level for any discount factor & [0, 1)