Question 11: Two people take tums removing stones from a pile of n stones. Each person may, on each of her turns, remove either one stone or two stones. The person who takes the last stone is the winner; she gets $1 from her opponent. Find the suhgame perfect equihh'ia of the games that model this situation for n = l and r: = 2. Find the winner in each subgame perfect equilibrium for n = 3, using the fact that the suhgame following player 1's removal of one stone is the game for n = 2 in which player 2 is the first-mover, and the suhgame following player 1's removal of two stones is the game fore = l in which player 2 is the rst mover. Extra credit: Use the same technique to find the winner in each subgame perfect equilibrium for n=4,and,ifyoucan, foranarbitraryvalue ofn