There is a battle between two generals. General X (the column player) has two infantry units that he can send to any pair of locations. His strategy (1,4) for example means that he sends units to locations 1 and 4. General Y (the row player), on the other hand has only one infantry unit that he can send to either of the four locations. Thus, his strategies are 1,2,3 and 4.

(a) Suppose that General X does not send both units to one location. A unit wins a location if it arrives uncontested, and a unit fights to a standstill if an enemy unit also comes to the same location. A win generates one unit of utility, while a defeat or a standstill yields zero utility. Present the game in a strategic form and write the payoff matrix. Determine the best response for each general and determine the Nash equilibria for this game.

(b) Suppose that locations 1 and 2 are more valuable than locations 3 and 4. Winning locations 1 or 2 provides twice as much utility as locations 3 or 4. Present the game in a strategic form. Determine the best response for each player. Determine the Nash Equilibria of this game.