PRISONER'S DILEMMA EXPLAINS SPORTS DOPING (II of IV)

Scientific American Magazine - By Michael Shermer

Game theory helps to explain the pervasive abuse of drugs in cycling, baseball and other sports.

Game theory is the study of how players in a game choose strategies that will maximize their return in anticipation of the strategies chosen by the other players. The “games” for which the theory was invented are not just gambling games such as poker or sporting contests in which tactical decisions play a major role; they also include deadly serious affairs in which people make economic choices, military decisions and even national diplomatic strategies. What all those “games” have in common is that each player’s “moves” are analyzed according to the range of options open to the other players.

The game of prisoner’s dilemma is the classic example: You and your partner are arrested for a crime, and you are held incommunicado in separate prison cells. Of course, neither of you wants to confess or rat on the other, but the D.A. gives each of you the following options:

1. If you confess but the other prisoner does not, you go free and he gets three years in jail.
2. If the other prisoner confesses and you do not, you get three years and he goes free.
3. If you both confess, you each get two years. 4. If you both remain silent, you each get a year.

Consider the choices from the first prisoner’s point of view. The only thing the first prisoner cannot control about the outcome is the second prisoner’s choice. Suppose the second prisoner remains silent. Then the first prisoner earns the “temptation” payoff (zero years in jail) by confessing but gets a year in jail (the “high” payoff) by remaining silent. The better outcome in this case for the first prisoner is to confess. But suppose, instead, that the second prisoner confesses. Then, once again, the first prisoner is better off confessing (the “low” payoff, or two years in jail) than remaining silent (the “sucker” payoff, or three years in jail).

Because the circumstances from the second prisoner’s point of view are entirely symmetrical to the ones described for the first, each prisoner is better off confessing no matter what the other prisoner decides to do. Those preferences are not only theoretical. When test subjects play the game just once or for a fixed number of rounds without being allowed to communicate, defection by confessing is the common strategy. But when testers play the game for an unknown number of rounds, the most common strategy is tit-for-tat: each begins cooperating by remaining silent, then mimics whatever the other player does.

Even more mutual cooperation can emerge in many-person prisoner’s dilemma, provided the players are allowed to play long enough to establish mutual trust. But the research shows that once defection by confessing builds momentum, it cascades... throughout the game.

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