The EU and the US sign a trade agreement which restricts each party to set a tariff of at most 10% on bananas and cheese, respectively. Denoting the tariff by x for the EU and by y for the US, in light of the new trade policies the payoff to the EU is calculated as

12 + 2x 4y + xy x2 and the payoff to the US is calculated as

16 11x + 4y + 2xy y2 The tariffs are set simultaneously.

(a) Find the best response functions and display them in a graph.

(b) Calculate the Nash equilibrium tariff levels in this game.

(c) Show that both the EU and the US would be better off without the tariffs.

(d) Since the trade agreement is new and the norm used to be to set much higher tariffs, if there is no explicit coordination between the two parties then they may not choose their Nash equilibrium tariff levels. Suppose that both the EU and the US knows that the other one is going to set the tariff in a rational manner, but that this is not common knowledge. What is the set of tariffs for each party that is consistent with this assumption? (Hint: this means that both parties know that the other one uses only best responses, but neither knows that the other one knows this about them.) Is the Nash equilibrium tariff level consistent with this assumption for the two parties?