UBC mathematician says game theorists will be paying attention to World Cup

The FIFA World Cup, which begins on June 12, will capture the attention of hundreds of millions of soccer fans. It will also pique the interest of economists and computer scientists who study game theory, the study of strategic decision-making.

Game theorists have studied penalty kicks and found that the behaviour of soccer players is strikingly consistent with Nash equilibrium, a theory made famous in the 2001 film A Beautiful Mind. It asserts that kickers and goalkeepers will follow predictable strategies for trying to outwit each other.

Kevin Leyton-Brown, an associate professor in UBC’s Dept. of Computer Science who also helped create a free online course on game theory, explains how famed footballers like Lionel Messi, Cristiano Ronaldo and Iker Casillas are not just world-class athletes; they’re also remarkably rational decision-makers.

How do penalty kicks support the idea of Nash equilibrium?

Kickers and goalies have to make decisions simultaneously because things happen so fast. They have to decide to go right or left or in the middle.

On top of that, kickers are usually better at kicking to one side than the other. You would think that the kicker would always kick to his stronger side, but if he did the goalie would always jump to that side and the kicker would be worse off. So a kicker, like someone who bluffs in poker, sometimes has to pick the lesser option and kick to his weak side to make goalies uncertain of what he’s going to do.

What researchers found when they looked at this publicly available data was that kickers and goalies usually pick their equilibrium strategies. Kickers kick to their weak side just often enough so that the goalie doesn’t always want to jump the same way. Likewise, goalies picked an equilibrium strategy for blocking shots.

It’s a really beautiful vindication for a mathematical theory that was described in very abstract terms.

What is the Nash equilibrium?

John Nash was thinking about interactions between multiple self-interested people and how to predict what they would do in a strategic interaction with each other.

Every single game or strategic interaction between two or more people that has a finite number of choices has a Nash equilibrium, which is a stable strategy for all sides.

The word equilibrium connotes balance. I can’t do better than I’m doing, given what you’re doing; you can’t do better than you’re doing, given what I’m doing. We’re both in balance. That is the core of Nash equilibrium. This is what happens with penalty kicks.

Why is game theory important?

It’s about trying to predict how rational people will make decisions. There are a huge number of applications. The most common are in economics, which is fundamentally the study of how to make good decisions in a society. It applies to things like how to hold an auction or a referendum. It’s also important for computer scientists, who may want to build a computer network that’s going to be used by many people at the same time. The performance of these things depends on how other people use them, so game theory is important.

Will you be watching the World Cup?

How can you not get caught up in the World Cup? The stakes of these games and penalty kicks are so high. Players can feel the immediate reward of scoring a goal, but also the immense shame of missing a penalty kick that’s really important.

Kevin Leyton-Brown, along with Matthew Jackson and Yoav Shoham of Stanford, developed a Massive Open Online Course on game theory that is available on Coursera.