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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 Spring '12
 daniel
 Game Theory, partner, player

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