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Question

There are two fishing spots, one hot (H) and one cold (C). The hot spot has 20 fish, whereas the cold spot has only 12 fish. There are two fishers 1 and 2. A fisher can go to either spot to fish, but obviously only to a single spot. If the two fishers go to the same spot, they divide the catch equally. Assume linear utility functions. Show the normal form of the game. Does any player have a dominant strategy? Find the Nash equilibria of the game. How many NE of the game are there? Is the game symmetric? Justify your answer. Find the mixed strategy Nash equilibria of the game using the players best response functions. Check that your response is correct allowing one player to use pure strategies and the other to use mixed strategies. Let p = prob that F1 chooses the Hot spot and q = the probability that F2 chooses the hot spot. Are the fishers better off playing pure or mixed strategies? Explain. Now suppose that a third fisher wants to fish. Assume that the number fish in spots are the same. Let the number fish in the spots remain the same. For question find the mixed strategy equilibrium letting one player use pure strategies while the other two players use mixed strategies. For the calculations use the following convention: p = prob that P1 chooses the Hot spot; q = the probability that F2 chooses the Hot spot and r = probability that P3 chooses the Hot spot. Show that all three probabilities are equal in the mixed strategy Nash equilibrium. Answer the following questions Show the normal form of the game. Does any player have a dominant strategy? Find the Nash equilibria of the game. How many NE of the game are there? Is the game symmetric? Justify your answer. Find the mixed strategy Nash equilibria of the game. Are fishers better off playing pure or mixed strategies? Explain.

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