Reference no: EM133302452

Two people who earn money by fishing, labelled ?? = 1,2 are considering the number of hours per day to go fishing. Each person can choose any number of hours (including partial hours). The revenue generated for each person per hour of fishing is given by ?? (h1, h2) = 20 - h1 - h2 where h?? is the number of hours spent fishing by person ??. Each person's hourly cost of fishing is 2.

1. Explain why, when deciding on how many hours to fish, person 1 and person 2 are playing a game. Write down the payoff functions for each person and, explaining your reasoning, derive their reaction functions. Using words and mathematics, explain whether this is a game of positive or negative externalities.

2. Suppose fishing decisions are made simultaneously. Explaining your reasoning, determine the equilibrium number of hours spent fishing and payoffs in the game.

3. Suppose each person is restricted to fish for exactly 4.5 hours. What are each person's payoffs? Discuss this result with reference to externalities, the `tragedy of the commons' and the 'prisoners dilemma'.

4. Suppose now that person 1 has the right to go fishing before person 2. Person 2 can only go fishing after person 1 has come back and so observes the number of hours person 1 chooses. Explaining your reasoning, determine the equilibrium number of hours spent fishing and payoffs in this sequential-move game.

5. Using your answer to part (d), discuss whether there is first mover or second mover advantage. What would happen to each person's payoffs if, after person 1 chose his subgame perfect equilibrium hours, person 2 then chose his equilibrium hours from part (b)? Explain why person 2 threatening to do so is an incredible threat. Explain in words (no calculation is required), how person 2 could make the threat credible.