Two super-powers, A and B, are fighting for supremacy over the Atlantic Ocean. In order to simplify the problem, we consider their conflict over the control of two islands in the Atlantic Ocean. A currently possesses 3 armies while B possesses only two armies. A strategy for each super-powers consists of allocating a certain number of armies to take on battle in one of the islands. For example, A can choose to allocate two armies to Island 1 and one army to Island 2. Note that they can choose not to allocate any armies to a given island. Under the assumption that all armies are equally skilled, if A and B allocate the same number of armies to a given island they end up in a draw. This means that neither country controls the island and their reward is equal to 0. If one of the super-powers allocates a larger number of armies to a given island, it gains control of the island. In this case, we will assume that its reward is equal to 1 (and the penalty of the other country is -1). Hence, this is a zero-sum game where each super-power seeks to maximise its reward. 1. Formulate the situation described above as a zero-sum game. Find the optimal strategy for each player and the value of the game. 2. Assume that country A has the option to obtain an additional army. How would this improve their success in conquering islands? [measure this improvement in the increase of the value of the game for A]