Two fishing companies, Company A and Company B, each owns a fishing vessel and both have to decide whether sending their fishing vessels to North Sea or South Sea to catch fish. If both companies send their vessels to North Sea, each vessel can catch 150 tons of fish. If both companies send their vessels to South Sea, each vessel can catch 100 tons of fish. If one company sends its vessel to North Sea and the other company sends its vessel to South Sea, the vessel at North Sea can catch 250 tons of fish while the vessel at South Sea can catch 150 tons of fish. The price of fish is dependent on the total catch of fish. The price will be $200 per ton if the total catch is 200 tons, $150 per ton if the total catch is 300 tons and $110 per ton if the total catch is 400 tons. To both companies, the cost of catching fish at North Sea is $16,000 while the cost of catching fish at South Sea is $11,000.

(a) If both companies were to make a decision simultaneously, construct the payoff matrix in terms of profit of both companies as the payoffs. Apply the concept of simultaneous game and explain how you derive at the Nash equilibrium. Analyse whether the game is a prisoner's dilemma game. (20 marks)

(b) If Company A has the right to send its vessel first, construct the decision tree diagram and apply the roll back method to solve the sequential game. Explain how you derive at your answers and whether there is a first mover advantage in the game. (10 marks)

(c) Give a real life example of game theory which you encountered in a market. Describe and analyse the behaviour of the participants of the game with reference to the concepts you have learned. (10 marks)