Workings needed

Q n estion 2 Two timber companies. Alpha and Beta, have to decide whether to harvest timber om the North Hill or the South Hill and then sell the timbers in the same market. If both harvest om North Hill. each company can harvest 100 tons of timber. If both companies harvest om South Hill. each company can harvest 150 tons of timber. If one company harvests om North Hill and the other harvests from South Hill. the company at North Hill can harvest 150 tons of timber 1while the company at South Hill can harvest 250 tons of timber. The price of timber is dependent on the total supply of timber in the market. The price will be 51312} per ton if the total supply is EDD tons. 5150 per ton if the total supply is 300 tons and Sl per ton if the total supply is 4'00 tons. To both companies, the cost of harvesting in North Hill is Si and the cost of harvesting in South Hill is S l. (a) If Alpha and Beta were to make a decision simultaneously. construct the payoff matrix in terms of profit for both companies. Apply the game theory concept and solve for the Nash equilibrium and explain whether the game is a prisoner's dilemma game. {15 marks} {13) If Beta has the right to decide first and Alpha then can make a decision, construct a decision tree diagram in terms of prot and apply a roll back method to solve for the solution. {10 marks}