ECN 166  Game Theory
Fall, 2008
Homework Assignment 1
Solutions
1. Given the problem description we can construct the game tree as follows:
2. The game tree is given below. Note the following payo/s structure is used: for each
day that a student is wrong, he receives 1 (ie. he loses 1 pt) and for every day that
he is correct, he receives 1 pt. The opposite is true for the Professor. Therefore, more
points can be gained if the game is played longer. (This is just one interpretation of
the payo/s to each player.)How to read the tree:
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The professor is the °rst mover, choosing whether to schedule the test on Monday,
Wednesday, or Friday. The second mover is the student who doesn±t know which day
the test has been scheduled. On Monday, he must decide whether the test is today
or later.
If the test was, in fact, scheduled for Monday, the game ends and payo/s
to the professor and student are given accordingly.
If the test wasn±t scheduled for
Monday, the game continues. On Wednesday, the student must again decide whether
the test is today or later.
Again, if the test is scheduled for Wednesday, the game
ends.
Otherwise, the game continues onto Friday where the student faces the same
decisions. But since the test must be scheduled for one of the three days, and it hasn±t
already happened, the student knows for certain that the test will be scheduled for
Friday and will sensibly choose "Today".
The irrelevant decision "later" has been
removed from the Friday information sets. Note that the student has 7 information
sets. On Monday, the student doesn±t know whether the professor has scheduled the
test for Monday, Wednesday, or Friday. His decision nodes on Monday make up one
information set. On Monday, he decides whether the test will be "Today" or "Later".
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 Spring '08
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 Econometrics, Game Theory, Normal Form Game

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