Game Theory and Penalty Kicks
Soccer is the most widely played sports across the globe. This is a well-known fact, however what most people do not realize is that the penalty kicks can be modeled using Game Theory. The penalty kicks often are the most important part of the game because they frequently decide the outcome of many matches, including the world cup. The kicker and the goalkeeper play in a zero-sum game. A win for the kicker is a loss for the goalkeeper and vice versa. The kicker has two options to place the ball, left or right. Additionally, due to the speed and time constraints the goalkeeper must anticipate where the kicker will kick the ball. Thus, the goalkeeper must also choose left or right at the same time the kicker kicks the ball. The goal keeper does not have time to react, so he/she must choose a direction before the ball is kicked.
Dive Left (Goalkeeper) Dive Right
| Kick Right | 1,0 | 0,1 |
| Kick Left | 0,1 | 1,0 |
1 represents a wining outcome for either party. For the kicker 1 = goal. For the goal keeper a 1= save.
There is no pure strategy Nash Equilibrium because the goalkeeper wants to coordinate with the kicker, but the kicker does not want coordinate. In fact, the kicker does not want to have the same outcome as the goalkeeper. The best response for the goalkeeper if the kicker were to kick to the right would dive to the right. Moreover, the best response for the kicker if the goalkeeper were to dive to the right, would be to kick to the left. This represent an interesting situation because there does not exist a strict dominant strategy or an incentive for both parties to coordinate, only the goal keeper.
It’s very interesting to observe the intersection of game theory and sports. The information we learn in this class has widespread applications that can be understood in numerous contexts. A fundamental understanding of dominant strategies and Nash Equilibrium are critical to efficient decision making. For these reasons, understanding game theory is particularly relevant, especially in soccer penalty kicks.
Source: https://williamspaniel.com/2014/06/12/the-game-theory-of-soccer-penalty-kicks/