4. (15 p.) There are two piles of matchsticks on a table. At the start of the game, each pile contains 4 matchsticks. TWO players, Amy and Betsy, take turns removing matchsticks from the table; Amy goes rst. Whenever its her turn, a player must choose one pile, and must remove either 1, 2 or 3 matchsticks from that pile. The player who removes the last matchstick from the table is the Winner. If both Amy and Betsy are perfectly rational game theorists, Who Wins? Explain your reasoning: how should the Winning player play in order to guarantee the Win? (Answers Without satisfactory explanation get 0 points)