Beautiful Game Theory summary

The minimax theorem was introduced as far back as 1928, but had never been verified by empirical data. That is, until the penalty kick in soccer.

But why are penalty kicks considered a minimax game? Just like Rock Paper Scissors, there are only a limited number of strategies, which are chosen independently of the opposition’s choice.

Not only does the penalty shoot-out shed light on game theory; it also provides us with a unique opportunity to analyze the psychological factors in competitive behavior.

Economists and psychologists look at the environment in which decisions take place in order to better understand those decisions. A penalty kick, for example, falls under the category of “tournament settings,” characterized by competition. Social scientists use these models to analyze other real-life competitive situations, like job promotions, and study what factors influence who wins.

Because both teams perform in front of the same audience and because the result of the penalty shoot-out determines who wins the match (i.e., they have the same stakes), we can ask: does kicking order in a shoot-out effect athletes’ performance? The result is astonishing:

Consider that between 1970 and 2014, the winning frequencies by team in both national and international competitions were 60.6 percent for the first team and 39.4 percent for the second.

One of the fundamental tasks in economics is to analyze how people make decisions. The soccer field provides a perfect environment to study how social pressure affects our decision-making.

For one, audience support of the home team applies social pressure to the referee. Because professional games are attended by up to 100,000 people, this pressure can be overwhelming and can lead to bias.

In spite of fear’s drastic effects on our behavior, it has only very recently been investigated in economic theory. How does risk change the behavior of consumers? And how do they manage this fear?

Fear is the result of the difference between subjective and objective probabilities of risk – people respond to subjective fear of a situation, not the objective risk. First put into an economic model by Becker and Rubinstein in 2013, it put forward two testable hypotheses:

Interestingly, the Becker-Rubinstein model can be verified by soccer data by looking at how violence and hooliganism affect ticket sales. The following data is from 45 seasons in the Spanish League, from 1951-1995. One hundred and sixty seven events were recorded that qualified as hooliganism and 334 matches were singled out in a before/after analysis.

Married people, for example, show the strongest reaction to acts of violence and hooliganism, due to their higher costs of overcoming fear. Indeed, studies found a 40 percent difference in the ticket renewal rate between singles and married individuals after one particularly violent soccer season.