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Help required with a Game theory question Consider the following social dilemma: An island has two reefs suitable for fishing (named A and B), and

Help required with a Game theory question

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Consider the following social dilemma: An island has two reefs suitable for fishing (named A and B), and there are 20 fishers who simultaneously decide at which reef to fish. If n fishers choose reef A, each of them catches 12-n/2 fish. If m fishers choose reef B, each of them catches 5-m /4 fish. Each fisher only cares about the number of fishes that he or she catches. 1. Find the pure-strategy Nash equilibrium of this game. 2. Calculate the total number of fish caught in this Nash-equilibrium. 3. The chief of the island provides 8 selected fishers with a license to fish at reef A. No other fishers are allowed to go to reef A. A selected fishers does not have to use the license (i.e., such a fisher can still go to reef B) but if he or she does, a tax of 3 fish is collected. The fish that are collected this way are distributed equally among the fishers without a license. Argue that with this arrangement all licensed fishers will go to reef A. Compare the resulting outcome with the one from the Nash-equilibrium: How many fish are caught in total? Are the licensed fishers better off then before? What about the unlicensed fishers

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