Contest Model -- Tullock Model Application: Use the following information to answer questions 1-6.

Two equally talented contestants (Bonnie and Clyde) are competing for the $1000 prize that comes from winning the Cross-fit games in Cleveland (you get $1000 if you win, but you would NOT need to pay your opponent if you lose). 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)

Bonnie does 3 training sessions and Clyde does 2. What is the probability that Bonnie will win?

Question 1 options:

1

3/5

1/2

1/4

2/5

Question 2 (0.5 points)

Bonnie does 3 training sessions and Clyde does 2. What is the expected value of the contest for Bonnie?

Question 2 options:

$750

$450

$300

$400

$1000

Question 3 (0.5 points)

Bonnie does 3 training sessions and Clyde does 2. What is the expected value of the contest for Clyde?

Question 3 options:

$300

$100

$150

$1000

$250

Question 4 (0.5 points)

How could you determine whether the allocation of training sessions is a Nash equilibrium?

Question 4 options:

Verify that both players cannot improve their payoffs by reaching a mutually beneficial agreement.

Verify that at least one player has a dominant strategy.

Verify that each player can improve his or her payoffs by selecting another level of effort, holding the effort of the other contestant constant.

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.

Question 5 (0.5 points)

Suppose now that Bonnie decreases her number of sessions from 3 to 2, while Clyde continues to do 2 sessions. How does the expected value of the contest change for Bonnie and Clyde?

Question 5 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 increases.

Bonnie's expected value decreases and Clyde's expected value decreases.

Question 6 (0.5 points)

Suppose again that Bonnie continues does 3 sessions and Clyde does 2. A third contestant, Floyd, enters the contest, and does 4 sessions. What is the probability that Floyd will win? 

Question 6 options:

4/9

3/4

3/7

1/6

2/5

Information

Contest Model Continued & Class Readings: Question 7-14 are related to theory predictions of the contest model as well as the findings in a series of class readings introduced in the lecture notes

Question 7 (0.5 points)

According to contest theory, when the prize decreases

Question 7 options:

Neither player changes her effort.

Only the less talented player puts forth more effort.

Both players put forth more effort.

Only the more talented player puts forth more effort.

Both players put forth less effort.

Question 8 (0.5 points)

According to contest theory, when the dispersion of prize increases, holding the total prize money fixed

Question 8 options:

Only the more talented players put forth more effort.

The more talented players put forth less effort, while the less talented players put forth more effort.

Only the less talented players put forth less effort.

Each player puts forth less effort.

Each player puts forth more effort.

Question 9 (0.5 points)

According to contest theory, when the number of contestants increases

Question 9 options:

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.

Each contestant puts forth less effort.

Only the more talented contestants put forth less effort.

Each contestant puts forth more effort.

Question 10 (0.5 points)

According to contest theory, when the contest becomes more asymmetric (the difference in ability increases)

Question 10 options:

Only the less talented contestants puts forth less effort.

All contestants put forth less effort.

The more talented contestants put forth more effort.

The less talented contestants puts forth more effort.

Each contestant puts forth more effort.

Question 11 (0.5 points)

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 better ranked team to put forth more effort.

Only the better ranked team to put forth less effort.

Only the worse ranked team to put forth less effort.

Both teams to put forth less effort.

Both teams to put forth more effort.

Question 12 (0.5 points)

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:

People run 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.

Horses runs faster in races where the prize is greater.

Question 13 (0.5 points)

According to the study on corruption in Sumo Wrestling, one of the fact that makes corruption possible is the repeated game nature of the wrestling tournament.

Question 13 options:

True

False

Question 14 (0.5 points)

According to the study on officiating bias in NCAA basketball, if referees are unbiased

Question 14 options:

The foul differential between home and away teams will have a chi-square distribution.

The foul differential between home and away teams will have a geometric distribution

The foul differential between home and away teams will always be zero.

The foul differential between home and away teams will have a student's t-distribution.

The foul differential between home and away teams will have a binomial distribution.

Information

Regression Results Interpretation: Use the following information to answer questions 15-20.

An interesting paper, “Crime on the Court” 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 and OFFICIAL measures the number of officials (i.e. referees).

Question 15 (0.5 points)

What is the dependent variable?

Question 15 options:

Intercept.

Number of fouls called in the game.

Time.

Number of referees.

Final score of the game.

Question 16 (0.5 points)

Which of the following best states the hypothesis that the authors want to test?

Question 16 options:

There are too many fouls called in the ACC.

Increasing the number of foul calls decreases the number of referees.

Officials have been getting stricter over time.

Attendance has no effect on the number of fouls called.

Increasing the number of referees decreases the number of foul calls.

Question 17 (0.5 points)

According to the regression results above, increasing the number of referees from 2 to 3

Question 17 options:

Increases the number of fouls called in games where less than twenty-one fouls are called.

Decreases the number of fouls by about 21.

Increases the number of fouls called in games where more than twenty-one fouls are called.

Does not have an effect on the number of fouls called.

Increases the number of fouls by about 21.

Question 18 (0.5 points)

Is the coefficient on OFFICIAL statistically significant at 1% level?

Question 18 options:

Yes because the p-value is positive.

No because the coefficient is larger than 0.01 (1%) 

Yes because the p-value is smaller than 0.01 (1%).

No because the standard error is larger than 0.01 (1%).

Question 19 (0.5 points)

Roughly how many standard deviations from zero is the coefficient on SCORE?

Question 19 options:

4.6

50

0.2

1

8

Question 20 (0.5 points)

The variable HITEDIFF measures the difference in height (in inches) between teams. In this study it is a

Question 20 options:

Omitted variable.

Fixed effect.

Dependent variable.

Dummy variable.

Control variable.

Question 21 (0.25 points)

BONUS: The lecture on side effects gives two examples -- American League Baseball's Designed Hitter Rule (DH) and FIFA's change in scoring system. According to the lecture, which of the following are intended effects of a rule change, and which are unintended side effects?

Question 21 options:

Increase number of yellow cards (Change in scoring system, FIFA).

More batters intentionally hit by the pitch (DH rule, American League Baseball).

Replace poorly hitting pitchers with better hitting DH's (DH rule, American League Baseball).

Encourage aggressive offense (Change in scoring system, FIFA).

1.

Intended effect.

2.

Unintended side effect.

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