2. a) ( Removing stones) Two people take turns removing stones from a pile of in stones. Each person may, on each of her turns, remove either one or two stones. The person who takes the last stone is the winner; she gets $1 from her opponent. Find the subgame perfect equilibria of the games that model this situation for n = 1 and n =2. Find the winner in each subgame perfect equilibrium for n = 3, using the fact that the subgame following player I's removal of one stone is the game for n = 2 in which player 2 is the first-mover, and the subgame following player I's removal of two stones is the game for n = 1 in which player 2 is the first-mover. Use the same technique to find the winner in each subgame perfect equilibrium for n = 4, and, if you can, for an arbitrary value of n