Game theory and drug taking in sport- Athletes, Organisers and Spectators

Lance ArmstrongDrug-taking in professional sport has long been a major concern and there is no better example than seven times Tour de France winner Lance Armstrong who admitted to doping. Furthermore in the period from 1997 until 2002 among 64 world class 100 metre sprinters 25% have been convicted of doping and this doesn’t include two American sprinters who tested positive this year. So why do athletes continue to dope eventhough you could get banned for life if caught?

Prisoners Dilemma to Inspection Game to Metagame

Game theory deals with differences of opinion between groups who know each other’s inclination but not their genuine objective or choice. It then concludes the optimum course of action for any rational player. In this scenario the parties involved are the competing athletes and although both are better off if neither takes drugs, they cannot trust each other so both engage in doping – Prisoners Dilemma. If you introduce an authoritative figure – the organisers – to test the athletes the fear of getting caught should ensure that athletes remain clean, referred to as the Inspection Game. However this cannot be said to happen at leading sports events as athletes, on the whole, don’t think they will get caught. Researchers from the University of Hamburg have introduced yet another party which they refer to as the customer (sponsor and spectators). Their critical role is the potential withdrawal of support which could see the sport’s demise. A withdrawal of one of these three parties can trigger the withdrawal of the other two. Sports events cannot survive without sponsors, withdrawal of the media restricts the access to the customers, and finally sport is only attractive for sponsors as long as there are customers. Therefore the strategies of the three parties looks like this:

Athletes – Dope or Clean (D C)
Organisers – Test or No Test (T N)
Customer – Stay or Leave (S L)

In the figure below organisers decide on the testing the athletes whether there was doping or not. But more importantly customers are to be informed about doping tests that turn out to be negative as well as positive. The customers then decide whether to stay or leave.

Tree - Game Theory

The assumptions are as follows:

D-N-S > C-N-S = athletes prefer to dope if not tested.
C-T-S > D-T-L = athletes prefer to be clean and tested = customers stay, over being doped and tested = customers leave (assuming that customers don’t like doping *scandals)

D-N-S > D-T-L = a scandal combined with a loss of customers is worse for organisers than undetected doping where customers stay.
C-T-S > C-N-L = testing clean athletes with customer support is better for the organisers than not testing clean athletes when customers leave.

D-T-L > D-T-S = customers prefer to withdraw support after a scandal
D-N-S > D-N-L = customers prefer to stay if there is no scandal.
C-T-S > C-T-L = customers prefer to stay if there is no scandal.
C-N-S > C-N-L = customers prefer to stay if there is no scandal.

*Dope & Test = Scandal
Dope & No Test, Clean & Test, Clean & No Test = No scandal

In reality customers who are ready to leave after doping scandals undermine the incentives to test athletes and find them guilty of doping. Consequently this encourages athletes to use performance- enhancing drugs and organisers to reduce their anti-doping methods in order to preserve the economic worth of the event – eg the Olympic Games.

Most athletes that have been found guilty of doping are not delinquent exceptions, but just unlucky scapegoats because the probability of being caught is low. The solution suggested would be to establish transparency so that the customer would know the results for all tests whether they were positive or negative. This allows the customer to condition their support on the presence of serious anti-doping tests. In practical terms this transparency could create a rating for each event based on how rigorous their anti-doping policy is.

Final thought

The vast majority of authorities in today’s sports events would state that their testing regimes were very stringent. However the likelihood of human deceitfulness is very realistic and in some cases it is not those that take the performance enhancing drugs who are the real cheats, but those who have generated an environment where athletes would be foolish not to.


Nobody’s Innocent – The Role of Customers in the Doping Dilemma. Berno Buechel et al. University of Hamburg. January 30th 2013

Athlete’s dilemma – The Economist Print Edition July 20th 2013

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