Two fishing vessels, Golden Catch and Silver Net, have to decide on which shore, the east or the west, to catch fish. If both vessels travel to the east shore, each vessel can catch 15 tons of fish. If both travel to the west shore, each vessel can catch 10 tons of fish. If one travels to the east shore and the other travels to the west shore, the east shore vessel can catch 25 tons of fish while the west shore vessel can catch 15 tons of fish. The price of fish depends on the total catch of fish. The price will be $2,000 per ton if the total catch is 20 tons, $1,500 per ton if the total catch is 30 tons and $1,000 per ton if the total catch is 40 tons. Travel to the east shore will consume fuel costs $5,000 while travel to the west shore will consume fuel costs $2,000. There are no other costs incurred except the fuel costs.

(a) If both vessels need to make decision simultaneously, construct the payoff matrix in terms of profits of both vessels as payoffs and solve for the Nash equilibrium. Analyse and explain whether the game is a prisoner dilemma game.

(15 marks)

(b) If Golden Catch has the right to travel first and Silver Net can then travel, construct and analyse the decision tree diagram and solve for the solution using roll back method. Did Golden Catch get any benefits from moving first compared to the case of simultaneous decision?