Laverne and Shirley, two equally talented athletes, expect to compete for the co

ID: 3008649 • Letter: L

Question

Laverne and Shirley, two equally talented athletes, expect to compete for the county championship in the 400 meter hurdles in the up-coming season. Each plans to train hard, putting in several hours per week. We will use the Tullock model to describe their behavior.

For each athlete winning is worth 20 hours per week; so we measure the prize as 20 hours. The cost of an hour of effort is, of course, one hour. The probability is as described in the Tullock model.

Suppose that Laverne plans to train 10 hours per week, and that Shirley plans to train 20 hours. What is the probability that Shirley will be the county champ?

P(Shirley wins)=20/(10+20) = 2/3

What is Shirley’s payoff? (i.e. prob x prize – cost) Note: the payoff is measured in hours, not money.

Suppose that she increases her training time to 25 hours per week. Does her payoff rise or fall? Explain.

Suppose that she reduces her training time to 15 hours per week. Does her payoff rise or fall? Explain.

Is the allocation where Laverne trains 10 and Shirley trains 20 an equilibrium? Why or why not?

Is the allocation where each athlete trains 5 hours per week as Nash equilibrium? (Hint: you can check to see if the payoff rises when, say, Laverne increases to 6 and then when she reduces to 4. You don’t have to check for Shirley’s incentives because the situation is symmetric.)

Number of hours for Laverne Payoff for Laverne

(assuming that Shirley trains 5 hours.)

4 __________

5 __________

6 __________

Finally, assume that the prize rises to 40 hours. Show that the 5 hours each allocation is no longer a Nash equilibrium. (Hint: you only have to check that the payoff is higher at 6 hours for Laverne (again, holding Shirley at 5 hours.)

One of the predictions of contest theory is that effort is greater in symmetric contests, where ability is relatively equal as compared to asymmetric contests, where ability is unequal. In “the incentive effects of leveling the playing field,” Franke tests this idea with data on amateur golf tournaments. The paper is here.

http://peer.ccsd.cnrs.fr/docs/00/67/07/63/PDF/PEER_stage2_10.1080%252F00036846.2010.537646.pdf

He compares performance when the score uses unadjusted scores versus those that adjusts score by handicap. (Handicap scoring levels the playing field for the lower ability golfer.) So, when the score is adjusted by handicap, we say that it is net or handicap. If the score is not adjusted, we say that it is gross.

Here is the distribution of performance difference in tournaments that use gross (unadjusted) vs net (adjusted). (Performance is measured using the Stabelford system. This sytem awards point values for scores relative to par. A better score earns more points, unlike the usual method of scoring in golf.

2 or more over par - 0 points

1 over par - 1 points

Par - 2 points

1 under par - 3 points

2 under par - 4 points

3 under par - 5 points

If there were no difference in performance, the distribution should be approximately binomial (bell-shaped) with a mean of zero..

Looking at the data, what is your guess about which type of tournament has higher (better) performance.

Is your answer to part a consistent with the predictions of contest theory? (Hint: the net score is a more even contest, in that the lower quality golfer has strokes subtracted from his or her score.)

The table shows regression coefficients (standard errors in parenthesis) for the independent variables. The dependent variable is score. (again, under the stabelford system higher is better).

Type is a dummy variable with 1 for net score tournaments and 0 for gross score tournaments. Explain the meaning of the coefficient.

Is it significant at the 5% level? Explain.

What is the t-statistic? ________________

The variable “female” is a dummy variable with 1 for female tournaments and 0 for male tournaments. The coefficient is positive, indicating that women perform better. Is this study evidence that women are better golfers? Explain.

Explanation / Answer

Ans-