Game Theory as it relates to Football
The concept of risk vs. reward lies at the heart of game theory. What is your anticipated result if you do action X in situation Y? is a question that social scientists unduly complicate and call “Subjective Expected Utility.”
The “Prisoner’s Dilemma” is the most well-known game theory competition. The Prisoner’s Dilemma is based on the idea that each of the two players is a potential criminal who has been arrested by the police and is being questioned. Police have sufficient evidence to find both players guilty of a relatively minor offense (which will lead to a short jail sentence for both). The authorities, however, require at least one of the players to confess in order to find them guilty of the more serious accusation; otherwise, they risk losing their chance at a pardon. Both suspects face a brief jail sentence if they both refuse to speak. If one suspect comes forward with a confession and the other doesn’t, the one who comes forward is let off the hook while the other is given a harsh prison sentence. If both suspects confess, both are sentenced to time in jail, but it is less time than each would have received had only one confessed.
The rational option for each player in a one-off version of the Prisoner’s Dilemma is always to “defect” — to confess to the authorities. This is due to the fact that, regardless of what the other player does, the outcome is always better for that player if he confesses.
However, when interactions are repeated (we refer to these as “iterated” or multi-round competitions since social scientists never use simple terms when complex ones will do), they are influenced by something known as “the shadow of the future.” The Evolution of Cooperation by Robert Axelrod, published in 1984, is my favorite book on game theory. Even if he was employed by the University of Michigan at the time it was written. According to Axelrod, patterns of cooperation can develop when players anticipate repeat interactions because the overall result will be better for both players than it would be if they were continuously backstabbing one another.
Sources:
https://www.offtackleempire.com/2022/10/2/23383277/on-game-theory-and-college-football
https://www.degruyter.com/document/doi/10.2202/1559-0410.1176/html
https://www.tandfonline.com/doi/abs/10.1080/14660970802008959