Information
Use the following information to
answer questions 1-7.
Two equally talented contestants
(Bonnie and Clyde) are competing for the $1000 prize that comes from
winning the Cross-fit games in Cleveland. We use the contest model
(Tullock model) to explain their actions. Measure effort as the number of
$50 training sessions that each contestant pays for. For instance, if Bonnie
does four training sessions, her effort cost would be $50 x 4 = $200.
Question 1(0.5 points)
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Bonnie does six training sessions
and Clyde does two. What is the probability that Bonnie will win?
Question 1 options:
4/5
1/2
2/3
1/4
3/4
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Question 2(0.5 points)
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Bonnie does six training sessions
and Clyde does two. What is the expected value of the contest for Bonnie?
Question 2 options:
$300
$1000
$750
$400
$450
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Question 3(0.5 points)
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Bonnie does six training sessions
and Clyde does two. What is the expected value of the contest for Clyde?
Question 3 options:
$1000
$0
$150
$100
$250
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Question 4(0.5 points)
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In a Nash Equilibrium of this
game, which of the following is true?
Question 4 options:
Neither
player can improve his payoffs unilaterally (without the other player
changing his move).
Each
player should play a mixed strategy.
The sum
of the players’ payoffs is maximized.
a. and
b. are true.
b. and
c. are true.
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Question 5(0.5 points)
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How could you determine whether
the allocation of training sessions is a Nash equilibrium?
Question 5 options:
Verify
that at least one player has a dominant strategy.
Verify
that both players cannot improve their payoffs by reaching a mutually
beneficial agreement.
Verify
that the player with the most training sessions wins the prize.
Verify
that neither player can improve his or her payoffs by selecting another level
of effort, while holding the other player’s effort constant.
Verify
that each player can improve his or her payoffs by selecting another level of
effort, holding the effort of the other contestant constant.
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Question 6(0.5 points)
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Suppose now that Bonnie decreases
her number of sessions from six to four, while Clyde continues to do two
sessions. How does the expected value of the contest change for Bonnie and
Clyde?
Question 6 options:
Bonnie’s
expected value increases and Clyde’s expected value stays the same.
Bonnie’s
expected value decreases and Clyde’s expected value stays the same.
Bonnie’s
expected value increases and Clyde’s expected value increases.
Bonnie’s
expected value decreases and Clyde’s expected value decreases.
Bonnie’s
expected value decreases and Clyde’s expected value increases.
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Question 7(0.5 points)
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Suppose again that Bonnie
continues does six sessions and Clyde does two. A third contestant, Floyd,
enters the contest, and does four sessions. What is the probability that Floyd
will win?
Question 7 options:
2/9
1/3
2/5
2/7
1/6
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Question 8(0.5 points)
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According to contest theory, when
the prize decreases
Question 8 options:
Both
players put forth less effort.
Only the
more talented player puts forth more effort.
Only the
less talented player puts forth more effort.
Neither
player changes her effort.
Both
players put forth more effort.
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Question 9(0.5 points)
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According to contest theory, when
the contest becomes more asymmetric (the difference in ability increases)
Question 9 options:
The more
talented contestants put forth more effort.
The less
talented contestants puts forth more effort.
All
contestants put forth less effort.
Each
contestant puts forth more effort.
Only the
less talented contestants puts forth less effort.
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Question 10(0.5 points)
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According to contest theory, when
the number of contestants increases
Question 10 options:
Each
contestant puts forth less effort.
Each
contestant puts forth more effort.
Only the
less talented contestants put forth less effort.
The more
talented contestants put forth less effort, while the less talented
contestants put forth more effort.
Only the
more talented contestants put forth less effort.
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Question 11(0.5 points)
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Suppose that the Big Ten told its
referees to call more fouls on the higher ranked team. According to contest
theory, we would expect
Question 11 options:
Only the
worse ranked team to put forth less effort.
Both
teams to put forth less effort.
Both
teams to put forth more effort.
Only the
better ranked team to put forth less effort.
Only the
better ranked team to put forth more effort.
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Question 12(0.5 points)
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According to the lecture on
races, which of the following is NOT one of the conclusions of research on foot
races, horse races, and dog races?
Question 12 options:
Horses
runs faster in races where the prize is greater.
Dogs run
faster in races that are closer.
People
run slower in races where the prize spread is greater.
Horses
run faster in races that are closer.
People
run faster in races where the prize is greater.
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Question 13(0.5 points)
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According to contest theory, when
the dispersion of prize increases, holding the total prize money fixed
Question 13 options:
Each
player puts forth more effort.
Only the
more talented players put forth more effort.
Only the
less talented players put forth less effort.
The more
talented players put forth less effort, while the less talented players put
forth more effort.
Each
player puts forth less effort.
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Question 14(0.5 points)
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According to the study on
officiating bias in NCAA basketball, if referees are unbiased
Question 14 options:
The foul
differential will have a student’s t-distribution.
The foul
differential will have a binomial distribution.
The foul
differential will always be zero.
The foul
differential will have a chi-square distribution.
The foul
differential will have a geometric distribution.
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Information
Use the following information to
answer questions 15-20.
An interesting paper, âCrime on the Courtâ
by McCormick and Tollison investigates the effect that the switch from two to
three referees in basketball had on the number of fouls called in a
game. For example, with more referees calling the game players may commit
fewer fouls out of fear of being caught.
They used data from the ACC
conference from 1954 to 1983. In 1978 the league switched from 2 to 3
referees. Here are some regression results from their paper.
In the table HITEDIFF measures the
difference in height (in inches) between teams, SCORE measures the
total score, ATTEND measures the attendance OFFICIAL measures the number
of officials.
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Question 15(0.5 points)
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What is the dependent variable?
Question 15 options:
Number
of fouls called in the game.
Intercept.
Final score of the game.
Time.
Number
of referees.
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Question 16(0.5 points)
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Which of the following best
states the hypothesis that the authors want to test?
Question 16 options:
Officials
have been getting stricter over time.
There
are too many fouls called in the ACC.
Increasing
the number of foul calls decreases the number of referees.
Attendance has no effect on the number of fouls called.
Increasing
the number of referees decreases the number of foul calls.
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Question 17(0.5 points)
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According to the regression
results above, increasing the number of referees from two to three
Question 17 options:
Increases
the number of fouls called in games where less than twenty-one fouls are
called.
Increases
the number of fouls by about twenty-one.
Does not
have an effect on the number of fouls called.
Decreases
the number of fouls by about twenty-one.
Increases
the number of fouls called in games where more than twenty-one fouls are
called.
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Question 18(0.5 points)
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The coefficient on OFFICIAL is
statisically significant at
Question 18 options:
At the
21% level, but not the 20% level.
At the
10% level, but not the 5% level.
At the
5% level, but not the 10% level.
At the
1% level.
No
commonly used significance level.
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Question 19(0.5 points)
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Roughly how many standard
deviations from zero is the coefficient on CHARGE?
Question 19 options:
One (1).
Fifty
(50).
Eight
(8).
Twenty
(20).
Four (4).
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Question 20(0.5 points)
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The variable HITEDIFF measures
the difference in height (in inches) between teams. In this study it is a
Question 20 options:
Dependent
variable.
Omitted
variable.
Control
variable.
Dummy
variable.
Fixed
effect.
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Question 21(0.25 points)
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BONUS: According to the lecture
on side effects, which of the following are intended effects of a rule change,
and which are unintended side effects?
Question 21 options:
12
Encourage
aggressive offense (Change in scoring system, FIFA).
12
More
batters intentionally hit by the pitch (DH rule, American League Baseball).
12
Replace
poorly hitting pitchers with better hitting DH’s (DH rule, American League
Baseball).
12
Increase
number of yellow cards (Change in scoring system, FIFA).