2 - ECON 3600 Problem Set 2(from the Yale Open Course in...

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ECON 3600 Problem Set 2 (from the Yale Open Course in Game Theory Problem Sets) You may work in groups of up to three students. Hand in ONE assignment for the entire group. Make sure to include the name and ID number of everyone in the group. Due Thursday, January 26. 1. Recall the voting game we discussed in class. There are two candidates, each of whom chooses a position from the set S i = {1, 2, 3,. .., 10}. The voters are equally distributed across these ten positions. So, 10% of the voters are at each position. Voters vote for the candidate whose position is closest to theirs. If the two candidates are equidistant from a given position, the voters at that position split their votes equally. The aim of the candidates is to maximize their percentage of the total vote. Thus, for example, u 1 (8, 8) = 50 and u 1 (7, 8) = 70. (Where u 1 (7, 8) means Player 1's payoff when Player 1 plays 7, Player 2 plays 8.) [Hint: in answering this question, you do not need to write out the full payoff matrices!] (a) In class, we showed that strategy 2 strictly dominates strategy 1. In fact, other strategies strictly dominate strategy 1. Find all the strategies that strictly dominate strategy 1. Explain your answer. [Hint: try some guesses and see if they work.] (b) Suppose now that there are three candidates. Thus, for example, u

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2 - ECON 3600 Problem Set 2(from the Yale Open Course in...

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