2. Consider the following game tree representing a deterministic two-player zero-sum game: H D bi B b2 d d2 e1 h 12 h a1 A E K F az C C1 G f f g1 82 M N mi mz n1 \ ^ ^ ^ A 4 6 2 3 4 8 9 5 2 4 3 2 1 1 9 In this game, players Max and Min alternate making moves in the following way: Max, Min, Max, Min. In other words, if a state is represented by an "up" triangle, then it is Max's turn to choose a move that will result in the next layer of nodes. "Down" triangles represent Min's turn. Each leaf node represents a position in which the game is over and is labeled with the corresponding utility. Max would like to end the game with the largest utility while Min would like to end the game with the smallest utility. a) Calculate the Minimax values of each state in the tree and write them next to their corresponding state names below: A = B = C = D = E = F = G = H = | = J = K = L = M = N = 0 = b) Assuming optimal play from both players, write which states will result from each player's turns below: Turn 1 (Max): Turn 2 (Min): Turn 3 (Max): Turn 4 (Min):