Two armies are fighting a war. There are three battlefields. Each army consists of 6 units. The armies must decide on how many units to place on each battlefield. They do this without knowing how many units the other army has committed to a given battlefield. The army who has the most units on a given battlefield, wins that battlefield, and the army that wins the most battles wins the war. If the armies each have the same number of units on a given battlefield , there is an equal chance that either army wins the battle. A pure strategy for an army is a list (U1, U2, U3) of the number of units it places on battlefields 1,2, and 3 respectively, where each Uk = 0,1,26 and the sum of the Uks is 6. For example, if Army A allocates its units (3,2,1) and Army B allocates its units (0,3,3), then Army A wins the first battle and Army B wins the second and third battles, and Army B wins the war.

a) Argue that this game has or does not have a pure strategy solution.

b) The actual solution to a game like this is inspired by the game Rock, Paper, Scissors. Analyze this proposition considering your analysis in part (a).

c) Based on (b) can you determine the best way for an army to make its decision?