Economics of Doping 101

In this short post I will show you that economics can be helpful in understanding doping in sport. I will start with a “textbook model”. In the following posts I will try to cover more complex cases.
Imagine there are two athletes competing for a prize of 1 million dollars on 100m dash. It is a one shot game, both athletes are similar in their natural performance, they can’t cooperate (they choose independently) and the only thing they care about is money. Each athlete can choose to dope or not, to take pill or not (a binary choice). Taking the pill significantly improves his athletic performance (in this case speed). If just one of the athletes dopes he will win for sure, If both of them dope, both of them can expect to earn 500k (50% probability of winning). Loser earns 100k for his participation. Using prohibited substances comes with two major costs, it damages health and it costs money. Let’s assume that those costs are expected to be 100k.

Each athlete will earn 400k if both dope (500k minus the costs of 100k). In this case, both athletes would be better off if no one dopes, they would not bear the costs of doping, i.e. they would both earn 500k net. The most profitable situation for each athlete is when he dopes and his competitor not (900k net profit for doper and 100k for non-doper).

Result of the game depends on the strategy each player chooses (dope or not). Matrix of all the possible outcomes is shown below. Each cell represents one outcome, the number on left corresponds to the profit of Athlete 2 (on the right to Athlete 1). There are altogether four possibilities, one possibility per one cell.


🏃Athlete 1
Dope 💊
 Not ❌
Athlete 2
400k ; 400k
 900k ; 100k
100k ; 900k

 500k ; 500k

How will this game end? 🤔 It is quite simple to find the right strategy for each player. Just look at the game from the perspective of Athlete 2. Whatever his opponent (Athlete 1) does, he is always better off when doped, because if Athlete 1 dopes, it is better for him to dope (500k > 100k). If Athlete 2 chooses not to dope, it is still better for Athlete 1 to dope (900k > 500k). Since both players are the same, they also have the same strategy, therefore the games ends in the situation where both athletes cheat!

Are the athletes happy about the result? Not really. They could be both better off if no one dopes (+100k dollars for both). Unfortunately, this will never happen, since it is in the best interest of each individual to cheat. This constitutes an economic problem, because the outcome is sub-optimal for both athletes.

To change the outcome of the game the costs of doping would have to increase to at least 500k (100k + 400k of extra costs) in order to make the doping strategy not profitable any more. The following matrix shows the new situation. Being clean is suddenly a better option for both athletes.

🏃Athlete 1
 Dope 💊
 Not ❌
Athlete 2
 0 ; 0
 500k ; 100k
 100k ; 500k
 500k ; 500k
The million dollar question is how to increase the costs of doping in such a way that doping becomes unprofitable. Economics of crime offers two ways, increasing either the probability of being caught and/or punishments (ban/financial penalty). Those two ways are to some degree interchangeable, it is assumed that you can achieve the same level of deterrence by different combinations of those two parameters.
Currently, there isn’t much space for an increase on the side of punishments because the system relies effectively only on bans. Unfortunately, financial penalties are very difficult to implement and enforce on a global basis. The only option for anti-doping authorities is thus investing a lot of effort (and money) in increasing the probability of detection. However, the history of anti-doping has taught us one important lesson, athletes and their personnel are very skilful in adapting to new anti-doping tests. The arms race among athletes and the subsequent fight against doping has triggered a second arms race, in this case between testers and dopers. In general, an arms race is detrimental for all of its participants. This has led many scholars and sport commentators to abandon the idea of fighting for “clean sport”. Basically what they argue is that one (inevitable) “arms race” is socially better than two “arms races”. Isn’t this argument a bit simplistic? 🤔 Yes, it is, the reality is much more complex and it is still possible that anti-doping in its current form creates net positive effects.. let’s hope for that… 🙏
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