The NFL just dished up a great example of Game Theory

When it comes to decision making and human behavior, few concepts spring to mind as frequently as the Prisoner’s Dilemma. A part of Game Theory, the Prisoner’s Dilemma describes how under certain circumstances, two people may take actions which do not make rational sense and may ultimately work against their own interests. The traditional example is two arrested people who are being interviewed by law enforcement and have to chose their next action, with the following options available:

• If Person A and B stay silent, both get 2 years in prison
• If Person A incriminates Person B and Person B stays silent, Person A goes free and person B gets 10 years in prison
• If Person B incriminates Person A and Person A stays silent, Person B goes free and person A gets 10 years in prison
• Both Person A and B incriminate each other, both get 5 years in prison

It is also taken into account that neither party has the ability to coordinate or co-operate on a decision prior to this example, leaving just their ability to infer on the other party's intent based on previous interactions with them. Reading these options, the risk minimsing option would seemingly be for everyone to stay silent, but in order to do so the individuals need to be assured the other would do the say. So out of fear for what the other inflict on them, both people incriminate each other and end up with more than double the prison time.

Of course in the real world, there is always a plethora of additional variables that prevent individuals from acting in a manner that would be called strictly rational. This means that real world examples of the Prisoner’s Dilemma are not always easy to come across.

However, through a series of unexpected events, the National Football League just provided one of the best real world examples of the Prisoner's Dilemma that will appeal to any lover of sports (or of real world examples for decision making theory….)

But first, a disclaimer. I need to make it clear that I am by no means an expert on the NFL, its rules or the machinations of how teams go about play making decisions, which of course may affect how this analogy is interpreted.

In the final regular season week of the NFL several teams were still yet to secure a spot in the playoffs, or be eliminated from contention. I won’t go into detail but the following unexpected things happened:

• The Indianapolis Colts, suffered a historic and shocking collapse against a lowly Jacksonville Jaguars team to be a surprise elimination from the playoffs.
• The Pittsburgh Steelers beat the Baltimore Ravens in overtime to keep their playoff hopes alive (as the Colts lost), depending on the outcome of the last game of the season between the Los Angeles Chargers and the Las Vegas Raiders

It is this final game that gave a wonderful real world example of the Prisoner's Dilemma.

Simply put, as all other teams had played their games, it became apparent that an “unthinkable scenario” could play out in which if these teams (the LA Chargers and Las Vegas Raiders) played to a tie, they would both go through and Pittsburgh would be eliminated.

This outcome looked like it was going to be avoided until an incredible final drive by the Chargers that resulted in a Touchdown right at the end (like 0.0 on the game clock) of the 4th Quarter, tying the game and setting up overtime. In the NFL, overtime is played for 10 minutes (regular season), at which point the team winning is declared the winner. However the first team to score a touchdown at any time automatically ends overtime and wins the game.

This meant that, in the final period of (overtime) play for the NFL regular season, the following outcomes could happen.

• LA wins, resulting in Pittsburgh progressing and Vegas being eliminated
• Vegas Wins, resulting in Pittsburgh progressing and LA being eliminated
• LA and Vegas end overtime in a tie, resulting in both teams progressing and Pittsburgh being eliminated.

One of the interesting play mechanics in the NFL is that teams can end their offensive plays by “taking a knee”, which if done enough times in a row will turn the ball over to the other team. This gives us a great example of the Prisoner’s Dilemma because of the options available to each team:

• LA takes a knee at the start of overtime, turning the ball over to Vegas, who then also takes a knee. Overtime runs out and both teams progress
• LA takes a knee, turning the ball over to Vegas, who then initiate an offensive play and go for the win. This could result in Vegas winning and LA being eliminated.
• Vegas takes a knee, turning the ball over to LA, who then initiates an offensive play and go for the win. This could result in LA winning and Vegas being eliminated.
• Both teams play offense as expected, resulting in overtime playing out as intended with one winner and one loser.

Ultimately, both teams opted for the final option and played overtime as expected, with the Las Vegas Raiders securing the win. Like all real world examples of theory, it is not perfect, but it does provide an illustration of two parties that can choose to cooperate for mutually assured gain and choose not to. Now of course, other factors like playoff seeding need to also be taken into account, as does the fact that neither team has the ability to coordinate an outcome.

It would have been a national scandal if it emerged that both teams agreed to play for a tie, tantamount to match fixing in many respects. Also, like in the traditional example, it would also have been impossible for both teams to be assured the other would keep their word and not try to go for the win. Furthermore, if the first team to have an offensive play did not “take a knee”, the opposing team would see that at a single to not take one either. This would effectively forfeit them of the chance to do so, even if they had intended on signaling to play for a draw.

Beyond being an exciting and truly unexpected way for the regular season to end, the NFL has just dished up a great example of how just because something may seem a logical choice on paper, doesn’t mean it will be in the real world.

Why? All you need to do is ask any economist or equities analyst and they will tell you that humans are not known to behave in a rational way, and to expect them to do so is foolish/.