This paper circulates around the core theme of Assume that the prize falls to 50 hours. Show that the 25 hours each allocation is no longer a Nash equilibrium. Hint: you only have to check that the payoff is highest at 24 hours, 25 hours, or 26 hours for Laverne (again, holding Shirley at 25 hours.) together with its essential aspects. It has been reviewed and purchased by the majority of students thus, this paper is rated 4.8 out of 5 points by the students. In addition to this, the price of this paper commences from £ 99. To get this paper written from the scratch, order this assignment now. 100% confidential, 100% plagiarism-free.
1. 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 100 hours per week; so we measure
the prize as 100 hours. The cost of an hour of effort is, of course, one
hour. The probability is as described in the Tullock model.
a. Suppose that Laverne plans to train 40 hours per week, and that
Shirley plans to train 20 hours. What is the probability that Shirley
will be the county champ?
__________
b. What is Laverne’s payoff? (i.e. prob x prize – cost) Note: the payoff is measured in hours, not money.
___________
c. Suppose that Laverne decreases her training time to 30 hours per week. Does her payoff rise or fall? Explain.
d. Suppose that Laverne increases her training time to 50 hours per week. Does her payoff rise or fall? Explain.
e. Is the allocation where Laverne trains 40 hours per week and Shirley trains 20 hours per week an equilibrium? Why or why not?
f. Is the allocation where each athlete trains 25 hours per week as
Nash equilibrium? (Hint: you can check to see if the payoff rises when,
say, Laverne increases to 26 and then when she reduces to 24. 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 10 hours.)
24 __________
25 __________
26 __________
g. Assume that the prize falls to 50 hours. Show that the 25 hours
each allocation is no longer a Nash equilibrium. Hint: you only have to
check that the payoff is highest at 24 hours, 25 hours, or 26 hours for
Laverne (again, holding Shirley at 25 hours.)
h. Finally, suppose that with the payoff back at 100 hours, a third
athlete, Edna, now enters the race. Edna has the exact same ability, and
the exact same payoff for winning the race, as Laverne and Shirley. Is
25 hours training each still a Nash equilibrium? Hint: Do the same thing
as before, that is hold both Shirley and Edna at 25 hours of effort.