Game Theory: Homework
Mathematics 170
due Friday, December 10, 2004
1. Mathematics and Politics, Chapter 7, page 184, problem 14. Hint: ei-
ther bor cis the second largest entry. Consider the two cases separately.
2. Suppose the utilities to Row of a game are
C N
C 2 -1
N 0 1
(a) If Row knew that Column would pick C with a probability of
100%, what should Row’s optimal strategy be? What utility
would Row expect from this strategy?
(b) If Row knew that Column would pick C with a probability of 25%,
what should Row’s optimal strategy be? What utility would Row
expect from this strategy?
3. Suppose we model the current conflict in Ukraine between supporters
of Yushchenko and Yanukovych as a game. Let’s say Yanukovych (who
is already in power, and who won the disputed election) can either call
for new elections or simply claim power. Let’s say Yushchenko can
either attempt to gain power through protesting, or concede defeat.
The utilities of the outcomes are:
•Yan. calls for new elections, Yush. concedes defeat: (+2 for Yan.,
-2 for Yush.)
•Yan. claims power, Yush. concedes defeat: (+6 for Yan., -10 for
Yush.)
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