This is a question on game theory and decision making in which the solution requires a decision tree

2. Consider the following game. Each of two players has a pile of stones. On alternate turns, each player places either one or two stones in a pile which is initially empty. Assume that player A goes rst and B second. a) Suppose that the player who places the fth stone wins the game. Draw the game tree, and use it to determine who will win. b) Can you determine who will win for any number of stones? Prove your assertion. (There is no need to draw the game tree!)