Consider the below game problem and answer the following questions: [3+5+1=9 Marks] MAX and MN are two players in the game, Rock-Paper-Scissors. Both players may choose any of the options Rock or Paper or Scissors by pressing buzzer button which is not visible to the other players. After both the players locks their options game point per round is awarded. There is one additional constraints that a player can't choose the same option in immediate consecutive rounds alone. Below is the rules of win or defeat, where an arrow from Paper to Rock is to be interpreted as PAPER DEFEATS ROCK. Scissors Cuts Paper The Paper Wraps Rock 102 Lozlov/ Rules Rock Blunts Scissors (a) Design appropriate utility function and construct game tree with utility up to level 4 or only two rounds per player. (b) Explain the process for speeding up the min-max search using the generated utility tree with alpha beta pruning. Show each step in the algorithm (C) If the above game where to be played by three players, suggest a suitable utility design and how the min-max algorithm could be customized to suit the change