Recall the "Fight Game" from Module 3. Two players must each choose a level of effort, e, between 0 and 1 without knowing the effort level of the other player, i.e. it is a simultaneous move game. If ei > ej then Player i gets all the surplus, S, and Player j gets nothing. The surplus is given by the function S = 2 - e1 - e2. If ei = ej then the players split the surplus equally. a. Show that the only Nash Equilibrium of this game is ei =ej=1. i. Step 1: show that any pair of strategies where 1 > e1 > e2 is not a NE. You may pick specific numbers for e1 and e2 if you like. (2 marks) ii. Step 2: show that any pair of strategies where 1 > e1 = e2 is not a NE. You may pick specific numbers for e1 and e2 if you like. (2 marks) iii. Step 3: show that 1 = e1 = e2 is a NE. (2 marks) b. What combination of strategies maximizes the surplus? Why is this outcome not attainable in this game? (2 marks) c. What classic game does this most resemble