How to catch a fraud in sports using game theory

August 4, 2020
posted in
written by Felix Brockerhoff & Daniela Richter

Without a doubt, whistle blowers are an important component for protecting the integrity of sports. However, few people dare to do “the right thing”.

His phone rings – unknown number. He is scared to death because of what he did yesterday. It was the only topic in the news today. He picks up. He hears rustling. He begins to sweat. Then he hears a “ka-ching”, 10.50 Euros please. He recognises the voice saying “thank you”. It is just a pocket call from his mum. He is relieved but nevertheless scared to the bone. What did our fictional protagonist Dave do?

Dave is a physiotherapist for a very successful Olympic team. He was part of a “performance initiative”, which organised the supply of performance enhancing substances to one of the athletes – illegal substances. The night before he eventually did what he was struggling with for three years already: Dave reported the work of, and everybody involved in, the performance initiative to the authorities. Dave is one of the whistle blowers who dares to tell the truth.

In the past, whistle blowers have exposed the best athletes and most important officials as frauds. Consider Chuck Blazar, principal witness in the FIFA corruption scandal, or Floyd Landis known as the “man who brought down Lance Armstrong”. Without a doubt, whistle blowers are an important component for protecting the integrity of sport. However, few people dare to do “the right thing”. Why did Dave hesitate so long? Let’s evaluate the decision of whistle blowing from a strategic, game-theoretical perspective, and see what possibilities authorities have to encourage the report of misconduct in the sports environment.

Game-theoretical analysis of reporting misconduct in sports

Let’s consider two games to evaluate different elements of Dave’s decision-making process. First, the Volunteer’s Dilemma (VD), which indicates that a better incentive scheme is needed for individuals to contribute to a public good, i.e. protect the integrity of sports. Secondly, the Prisoner’s Dilemma (PD), which shows that a situation should be created in which reporting is a dominant strategy.

In the Volunteer’s Dilemma more than two parties are involved. Any one of the individuals would have to make sacrifices in order to reach a better outcome for all individuals. If it is in the best interest of the majority to ensure fair sportsmanship, protecting the integrity of sports can be seen as a public good. Mechanisms to encourage reporting of misbehaviour should be implemented by reducing the sacrifice of the person reporting. The fear of prison sentence, unemployment, the reaction of team members and public pressure, are only some of the negative consequences Dave would face if he reported misconduct.

If only two parties were involved – Dave and the athlete – the strategic interaction could be structured similar to that of a typical Prisoner’s Dilemma, i.e. the fear of somebody else reporting earlier than Dave himself, and is part of his decision whether to report or not. However, the current incentive scheme favours the strategy of not reporting as already described. In order to use the mechanism described by the PD, the authorities should change the incentive scheme such that the likelihood of a team member reporting the misconduct is adequately high, i.e. blaming the other party becomes the dominant strategy.

There are two reasons why Dave hesitated so long to report the misconduct. The first is his sacrifice, which, by our definition, only occurs in the case of reporting. Since he knows about the severe disadvantages of reporting, he also knows that the likelihood of another team member reporting is low. Therefore, there is no situation as in the PD yet and the authorities would have to uncover the case themselves, for which the probability is low. Thus, the second reason why Dave hesitated is because the chance of being punished in case of not reporting is lower than in the case of reporting.

How to change the rules of the game – in favour of whistle blowing

The authorities could twist two screws to directly influence Dave’s behaviour. They could either change the probability of being punished or they could change the payoffs/sacrifice of Dave (i.e. the prison sentence). Let’s evaluate both possibilities in detail.

1. Change the probability of being punished

There are two ways to achieve higher reporting rates in the short term, by altering the likelihood of being punished. Firstly, the authorities could increase the likelihood of being caught when not reporting, by investing more resources in anti-doping controls. Secondly, the authorities could decrease, or eradicate, the likelihood of being punished if the whistle blower reports the misbehaviour (leniency programme). A credible signal from the authorities is needed here. A famous example is Sri Lanka, where the authorities granted all cricket players who reported doping during a given timeframe, no punishment. This would give Dave reassurance about the authorities behaviour if he reports.

 2. Change the payoffs/sacrifice of the whistle blower

Dave’s payoffs depend on his personal sacrifice. The punishment can be directly influenced by adjusting the underlying law. Politicians could increase the prison sentence if they reveal a misconduct without prior reporting. The other personal sacrifices can be softened by providing more certainty about witness protection programs. Those were famously necessary for the Russian whistle blower Witali Stepanow, who reported systematic doping in the Russian athletics team and now lives at an unknown location. This year, the German government announced that explicit external reporting offices will be implemented in order to reduce the barrier to report.

Using either one of the two possibilities has a direct and an indirect effect. Dave will be more inclined to report due to the new framework conditions (direct effect). Therefore, he knows that other confidants will be more inclined to report as well. This indirectly leads towards a stable equilibrium of whistle blowing, as this will turn out to be the dominant strategy (PD).


No matter what strategy the authorities decide to follow, it is important to send the right signal to the potential whistle blowers – if you report a misconduct that leads to conviction of a wrongdoer, the probability that you will be punished yourself is very low. There is also a system of witness protection for whistle blowers, and prison sentences for not reporting are very high. Using the example of whistle blowing in the world of sports, one can see how game theory can be used as a powerful tool to fundamentally change incentive schemes towards a politically desired action – reporting of misconducts!



Title image by Kristina Flour on Unsplash