ECO 383
Performance Enhancing Drug Examples
Fall, 2004
There are a couple of different ways that P.E.D. questions can be posed where strategic
behavior analysis is used as the basis for an answer. The first of these requires the use
game theoretic analysis to show various Nash equilibria. The second requires the use of
baseball specific information and deductive logic to arrive at a likely outcome.
1. Two players are competing for the same roster spot that will be awarded on the sole
basis of relative performance. Each can use a P.E.D. to increase his performance.
Assume that there are no adverse health consequences arising from using P.E.D.’s, the
players have equal abilities if they don’t use the drugs, and that although the league bans
theses substances, the sanctions and probabilities of detection are equal for both players.
Also assume that the effectiveness of the drugs is unequal. That is, the drug increases the
performance of player i by more than it increases the performance of player j. Finally,
assume that both player i, and player j are aware of this relative effectiveness disparity.
Given these assumptions find all possible Nash equilibria that result from a single period
game.
2. Two players of equal natural ability are competing for a single roster spot that will be
awarded solely on the basis of relative performance. One player is entering the 2nd year
of his career, and has little name recognition. The second is a veteran who is well
established in the league. Each can increase his performance by using a P.E.D. Also
assume the following:
a.
b.
c.
d.
e.
The P.E.D. is equally effective for both players.
The health effects of the P.E.D. are equal for both players.
The league bans P.E.D. use and punishes such use with a one-year expulsion.
The probability of detection for use is equal between players.
The veteran’s salary is greater than the 2nd year player’s salary.
Which of these two players is more likely to use a P.E.D and why is he more likely to do
so?