Question

1. Jacob and William, 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, the winning is worth 24 hours per week, so we measure the prize as 24 hours. The cost of an hour of effort is, of course, one hour. The probability is as described in the Tullock model [see page 5 of the slides "A Model of a Contest"]. d. Suppose that William reduces his training time to 10 hours per week. Does his payoff rise or fall (compared to part b)? Explain. Is the allocation where Jacob trains 10 and William trains 15 a (Nash) equilibrium? Why or why e. not? Is the allocation where each athlete trains 6 hours per week as Nash equilibrium? (Hint: you can check to see if the payoff rises when, say, Jacob increases to 11 and then when he reduces to 9. You don't have to check for William's incentives because the situation is symmetric.) f. Number of hours for Jacob Payoff for Jacob (assuming William trains 6 hours.) 6 7 Bonus question: Assume that the prize rises to 28 hours. Show that the 6 hours each allocation is no longer a Nash equilibrium.

Answer 1

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