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Two timber companies, Alpha and Beta, have to decide whether to harvest timber from the North Hill or the South Hill and then sell the timbers in the same market. If both harvest from North Hill. each company can harvest 100 tons of timber. Ifboth companies harvest from South Hill, each company can harvest 150 tons of timber. If one company harvests from North Hill and the other harvests from South Hill. the company at North Hill can harvest 150 tons of timber while 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 $180 per ton if the total supply is 200 tons. $150 per ton if the total supply is 300 tons and $100 per ton if the total suppiy is 400 tons. To both companies. the cost of harvesting in North Hill is $5.000 and the cost of harvesting in South Hill is $10,000. (a) If Alpha and Beta were to make a decision simultaneously. construct the payoff matrix in terms of prot 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. (1 5 marks) (b) If Beta has the right to decide rst 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. ( l 0 marks)