Creating a Game Out of Athletes Doping
https://mathsection.com/a-game-theoretic-analysis-of-doping/?cookie-state-change=1569200071140
One issue that has been prevalent and everlasting in all sports is performance enhancing drugs. Plenty of teams and individuals have faced serious consequences as a result of doping. Lance Armstrong, one of the most iconic Olympic cyclists of all time, had seven Tour de France titles stripped away from him in 2012. Tyson Gay, a star sprinter throughout the 2000s, tested positive for a banned substance and was suspended for a year and stripped of his silver Olympic medal. Even cases where doping was not confirmed creates serious stigmas around the team or individual’s name. For instance, Barry Bonds has never been suspended by the MLB and has been cleared of all charges related to PEDs, yet still for every record he has ever broken there is an asterisk next to it. So, then the question is, why do athletes still use banned substances? The article in the link above creates a game out of athletes doping to help explain why.
In order to create this game, we must first assume that every athlete’s goal is to win, and that they would rather win without doping than with doping. First, we will create the game under the circumstances that there are no negative consequences tied to taking PEDs. We will have two players, Player A and Player B, each of whom have 2 strategies: dope or no dope. Given these assumptions and circumstances, we have the following game with Player A on the left and Player B on the top.
| Dope | No Dope | |
| Dope | (2, 2) | (4, 1) |
| No Dope | (1, 4) | (3, 3) |
No matter what B chooses, A will choose to dope. Similarly, no matter what A chooses, B’s greater payoff is to dope. Thus, the Nash Equilibrium and the dominant strategy is both players A and B doping, even though they would both be happier if neither of them chose to dope. Thus, we must change the game so that it is optimal for both players to choose not to dope. Suspensions, revoking awards, and other consequences that are put in place create outside factors that change the payoff structure. For instance, if the consequences were very severe and the probability of getting caught very high then no one would choose to dope because the payoff would be way closer to 0 than to 2 at that point. While consequences can be made severe, it is currently impossible to catch every athlete that is using PEDs. As a result, every athlete has a decision to make, and they use this game to make that decision, whether it is consciously or subconsciously. Athletes that value the advantage on their component over the consequences and risk of getting caught will be those that choose to dope.