Prisoner’s Dilemma in an NFL Game
Prisoner’s dilemma happens all the time in professional sports. Teams compete to win the championship at the end of a season, and the only way to compete for a championship is to get into the playoffs. A good enough record during the regular season gets a team into the playoffs, yet teams need to consider the matchups afterward. The good teams that are confident to make the playoffs will start considering the games they play. This is where the prisoner’s dilemma comes in. Seeding strategies are crucial to a team’s playoff run because it involves matching up with different teams. For various reasons, for example, teams don’t want to get eliminated that early, or it is more entertaining when the best teams engage in the championship round, the top seeds may not want to face each other at the early stages of playoffs. Therefore, teams may lose intentionally to get a seed where they can match up better in the playoffs.
As for teams barely making the playoffs will try to win as many games as possible, regardless of the seeding strategies. For example, two teams are tied with the same record in the same division and are playing the last game of the season against each other. The team that wins heads to the post-season, the other gets eliminated, and the season ends early. What would you do if you were one of the head coaches? Most of the time, people choose to win, as it is the optimizing outcome. This is true. However, there are some rare cases where when the game ends with a tie, both teams stay alive and head to the post-season.
In the last week of the 2021-2022 NFL season, the Los Angeles Chargers and the Las Vegas Raiders faced each other. Both teams tried to clinch a seed in the playoffs by winning this game. They had identical records, and they were evenly matched. Suppose the Jacksonville Jaguars beat the Indianapolis Colts earlier that day, the Chargers and the Raiders have the option to tie the game, and both head to the post-season. Below is the prisoner’s dilemma matrix for the Charger and the Raiders.
Chargers
play to win play to tie
Raiders play to win 0.5, 0.5 1, 0
play to tie 0, 1. 1, 1
If they both play to win, either team is a 50% chance to win since they are evenly matched. If they talked about playing to a tie before the game, and one team betrays the other, the one team that tries to win will go to the post-season. If both teams agree on tying the game, they will, theoretically, both head to the playoffs.
Source:
Beaton, Andrew. “How an NFL Game Became a Prisoner’s Dilemma.” The Wall Street Journal. Dow Jones & Company, January 7, 2022. https://www.wsj.com/articles/raiders-chargers-tie-nfl-playoff-scenarios-11641516938.