Two timber companies, Alpha and Beta, have to decide whether to harvest timber from the North or 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. If both companies harvest from South Hill, each company can harvest 150 tons of timber. If one company harvests from the 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 supply is 400 tones. To both companies, the cost of harvesting in North Hill is $5000 and the cost of harvesting in South Hill is $10000.

1. 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.

1. If Beta has the right to decide first and Alpha then can make a decision, construct a decision tree diagram in terms of profit and apply a roll back method to solve for the solution