Strategic Behavior – Spring 2012
Homework Assignment 1 - Answers
Due: Wednesday, February 1, 2012
This homework assignment is based on the material in chapters 1 and 2 of the course text
(Harrington). Please ensure your assignment is legible!
1.
Provide an example of strategic interdependence from a TV, radio, magazine, or Internet
news source. Indicate the players, the strategies, and the objectives in this scenario.
Attach the citation or printed article.
Answer: The example should be attached. Each player should be indicated, and each player’s strategy
should be indicated (it is not sufficient to indicate strategies without indicating whose strategies they
are). Objectives must be included and attributed to each player (every player has to have an objective;
they must be stated separately). Payoffs should match the objectives given. This answer will differ
based on each student’s chosen scenario. Some common errors center on misunderstanding basic
terms.
2.
Diagram the extensive form representation of the scenario described in question 1.
Answer: This answer will differ based on each student’s chosen scenario.
3.
(Harrington Chapter 2, Question 2) Player 1 moves initially by choosing among four actions:
a, b, c, and d. If player 1 chooses anything but d, then player 2 chooses between x and y.
Player 2 gets to observe the choice of player 1. If player 1 chooses d, then player 3 moves
by choosing between left and right. Write down the extensive form of this setting (ignore
payoffs).
1
a
2
x
b
c
d
2
y
x
2
y
x
3
y
L
R
4.
Your professor’s syllabus clearly states no make-up exams will be given and no homework
assignments accepted late. Is she mean? Justify your response using strategic thought.
Answer: This question does not require a diagram. Suppose the professor is very kind. She
cannot, however, distinguish real excuses from lies, and also has difficulty judging reasonable
excuses. If students realize the professor is “soft”, they will procrastinate more and put
forward increasingly worse excuses. Deadlines then mean nothing and exam schedules become
chaotic. The result is an endless progression of uncertainty on both sides. The professor’s
refusal to accept all excuses is the only realistic alternative. The professor then avoids the
temptation to give in. Less pain is experienced by students and professor alike by denying
requests up front. Regardless of whether preferences are known, if students are aware of the
utility they will receive from the options available to them, they can make an informed decision
about the game they are playing.
Players: professor, students
Strategies:
Professor –
Accept assignments late
Enforce policy of no accepting assignments late
Students –
Procrastinate
Submit assignments on time
Objectives:
Professor –
Remain fair to all students
Take all reasonable measures to ensure students learn to be better citizens
Students –
Pass the course
Do as little work as possible
Maintain as much flexibility in scheduling as possible
Students
Procrastinate
Hand in work on time
Professor
Accept
4
2
Professor
Deny
Accept
2
3
3
4
Deny
1
1
There are two pure strategy equilibria: (1) procrastinate; deny/deny and (2) hand in on
time; deny/accept. This means: procrastinate and deny, and hand in on time and accept.
5.
There are three extensive form games shown on page 53 of the text. State which of them,
if any, violate the assumption of perfect recall. Explain your answer. We will discuss in
class, including the definition of perfect recall.
Answer: In game a, look at the information set for player 1 that contains two nodes. One is associated
with player 1 having chosen a and player 2 having chosen y, and one is associated with player 1 having
chosen b and player 2 having chosen x. At this information set, player 1 is not sure whether he chose a
or b, which violates perfect recall.
In game c, the information set for player 1 (which includes four nodes), shows that when player 1
chooses between actions c and d, she doesn’t know what player 2 chose (which is okay). However, she
also does not know what she chose at the initial node, which is in violation of perfect recall.
Game b is fine.