During the Allied invasion of France in 1944, the Germans had to decide where to place their defenses. They had three choices: they could concentrate their defenses at Calais, concentrate at Normandy, or split their defenses between both locations. The Allies had two choices: they could attack at Calais or at Normandy. Assume that this is a zero-sum game and that the possible outcomes are ranked as in the following matrix (where larger positive numbers represent outcomes more favorable for the Allies). German Calais Normandy Split Allies Calais 6, -6 2, -2 5, -5 Normandy 1, -1 4, -4 3, -3

(a) Are there any pure-strategy Nash equilibria for this game if the Germans and Allies move simultaneously?

(b) Suppose the Germans move first. Draw the game tree for this game and find the rollback equilibrium outcome.

(c) Suppose the Allies move first. Draw the game tree for this game and find the rollback equilibrium outcome.