Doping, Game Theory, and its Application in Sport

Game theory is a field that deals with strategic interactions between individuals in situations that involve cooperation or conflict. In other words, what would be my best strategy given the strategy of the other individual. But then the problem is Knowing that we know his methods, he will alter them. But knowing that he knows that we know that he knows, he might choose to return to his usual pattern. Sounds complicated, right? So, game theory is exactly about it.  It is also important to note that the main assumption about the individuals is that they are rational. In other words, they want to maximize their subjective expected utilities. Without going into the complicated analysis of what rationality is, here is the example. In Tokyo 2020 Olympics, the two best high jumpers finished the competition with exactly the same result. So, who gets the gold medal? There were two options on the table: This means that either each jumper has a probability of 50% to win a gold medal or each of them gets this gold medal with certainty. 

The decision to use doping, which not only provides an unfair advantage, but may also have serious health sequences. To better understand the decision to use doping, we have to understand the way athletes think about their future. For example, one study showed that professional athletes have biased time preferences.  The “win at all cost” orientation causes athletes to sacrifice their future in order to win in present. Given such a strong focus on “here and now”, game theory can easily predict that the usage of doping is actually an optimal choice. This is because a decision to dope is not only a decision that belongs to a single athlete. It is rather a coordination problem among all the athletes. Let’s consider a situation where two criminal suspects are taken into custody and separated such that they cannot communicate.

The district attorney tells them that he has not enough evidence to convict them in a trial. But several outcomes are possible. If one confesses and the other does not, the confessor will be released, whereas the other will be sentenced for a long time. If neither confesses, the attorney will have them both, taken in on a minor charge. If both confess, they will both be prosecuted but the attorney will recommend leniency. In fact, this is one of the famous examples in game theory. It is called a prisoners’ dilemma. So, what should the prisoners do?  Well, in general, among the possibilities available to the prisoners, they should choose the one that, whatever the other individual does, gives them the best deal than they would have gained by any other choice. This means that their optimal option is to confess.

However, this is not the best outcome for each of them. They could have been better off by choosing another strategy. This means that if coordination and joint action were possible, they could agree upon “not confessing” strategy and reach a better outcome. However, there is always a temptation to break the agreement and achieve an even better option. Thus, the joint “not confessing” option is an unstable solution. In the same spirit we can look at the choice to use doping in professional sport. Let us consider the following possible options. If both athletes dope, they are both have a 50% probability to win. The same if they both do not dope, which is of course better because they don’t harm their health in the long term.

However, if one of them dopes and the other sticks to the Fair Play, the cheater has a larger probability of winning. Thus, given that doping increases the chance of winning, the best choice is to dope. This is because even if the athletes agree not to dope, there is always a temptation to dope since it gives an advantage. This means that in order to fight doping, we need to use rational tools, so that the athletes would better off not to dope. The obvious one is to increase the risk of being caught. This is done by the increased number of tests of the current and previous tournaments. Second, is to increase the costs associated with being caught. 

One study even offered to introduce conditional pension funds from which the athletes can draw only after the end of their careers and only if they have never been caught doping. There are also possibilities of changing the prize structure. For example, a skewed prize structure where only a small fraction of athletes can win a prize may lead to more doping than a competition with many prizes. So, let’s hope for a clean sport. The athletes should understand that there is life also after sport.  It can be much healthier and happier without doping.