Problem 6. (The Colonel Blotto Game) Two armies are fighting a war. There are three battlefields. Each army cor must each decide how many units to place on each battlefield. They do this of units that the other army has committed to a given battlefield. The army given battlefield wins that battle, and the army that wins the most battles w have the same number of units on a given battlefield, then there is an equal that battle. A pure strategy for an army is a list (w1, #2, uj) of the number of 1, 2, and 3, respectively, where each it is in 0, 1,...,6 and the sum of the up allocates its units (3,2,1), and army B allocates its units (0,3,3), then army wins the second and third battles, and army B wins the war. 1. Argue that there is no pure strategy Nash equilibrium in this game. 2. Show that mixing uniformly at random over all possible configurations Nash equilibrium. (Hint: placing all units on one battlefield is not a go 3. Show that each army mixing with equal probability between (0,3,3), equilibrium