The Doping Game: Is It Rational for Athletes to Use Steroids?
The Doping Game: Is It Rational for Athletes to Use Steroids? On August 7, 2007, baseball player Barry Bonds hit his 756th career home run, surpassing the career record of 755 home runs by Henry Aaron. Although this should be a time of awe and praise for Bonds, the achievement continues to be tainted by allegations that his stellar performance was partially due to nei- ther skill nor hard work, but instead to performance-enhancing steroids. A re- cent book entitled Game of Shadows claims that Bonds engaged in significant steroid use beginning in 1998.
Regardless of whether Bonds is guilty or innocent, it is well recognized that doping is a serious problem in not only professional, but also amateur sports. The societal challenge is to design a system that deters athletes from using steroids. Such a system would be good not only for fans, but, more impor- tantly, the athletes themselves. Taking steroids is intended to give an athlete a relative advantage over other athletes, but if all athletes use them, then the ad- vantage is lost. Although the benefit evaporates, the cost remains, because ath- letes still suffer the health consequences. Game theory can be useful for
For the game shown in FIGURE 3.16, find the strategies that are consistent with the players being rational and each player believing that the other player is rational.
FIGURE 3.16
3.2 CHECK YOUR UNDERSTANDING
3,2 1,1
1,3
1,0
2,1
2,0
0,1
3,0 Player 1
Player 2
a
b
c
d
x
4,3
2,1
1,2
2,4
y
3,5
4,2
1,0
1,5
w z
investigating how to structure a system of monitoring and punishments to provide the right incentives.4
Although we’ll not take on that challenging task here, we can at least iden- tify the temptations faced by players and how they can affect their behavior. Consider a setting with three competitive athletes; think of world-class sprint- ers. They are assumed to differ in both innate skill and their propensity to take steroids (which could be determined by their desire to win). On the raw-skill dimension, suppose Maurice is faster than Carl and Carl is faster than Ben. As to the propensity to take steroids, Ben is more inclined to use them than Carl, and Carl is more inclined than Maurice. More specifically, Ben will take steroids regardless of whether Carl and Maurice do. Carl will not take steroids if no one else does, but in order to remain competitive, he’ll take them if either Ben or Maurice (or both) does so. Maurice, who is the fastest without per- formance-enhancing drugs, won’t take steroids unless both Ben and Carl do so.
These preferences are embodied in the strategic form game illustrated in FIGURE 3.17, where the first number in a cell is Ben’s payoff and the second number is Carl’s payoff. Maurice chooses a row, Carl chooses a column, and Ben chooses a matrix.
74 CHAPTER 3: ELIMINATING THE IMPOSSIBLE: SOLVING A GAME WHEN RATIONALITY IS COMMON KNOWLEDGE
FIGURE 3.17 The Doping Game
Ben chooses steroids
2,3,3 3,1,5
1,4,5 5,2,6 Maurice
Carl
Steroids
No steroids
No steroidsSteroids No steroids
Maurice
Carl
Steroids
No steroids
Steroids
Ben chooses no steroids
3,4,1 4,2,2
5,5,2 6,6,4
FIGURE 3.18 Steroids Is Ben’s Dominant Strategy
Ben chooses steroids
Carl
Steroids
No steroids
No steroidsSteroids
4,2, 2
6,6, 4
3,4, 1
5,5, 2
2,3, 3
1,4, 5
3,1, 5
5,2, 6 Maurice
Ben chooses no steroids
Carl
Steroids
No steroids
No steroidsSteroids
Maurice