Length Matters
When thinking about Game Theory we usually shift our thoughts to the very familiar Prisoner’s Dilemma. The Prisoner’s Dilemma is a game determining the best strategies for two prisoners who are unable to cooperate with each other. In the Prisoner’s Dilemma, it is presented that during the one-round game that it would be the most beneficial for both prisoners to “rat the other out.” However, in a real life scenario, there are multiple “rounds” where prisoners and interrogated multiple times, and in these cases prisoners usually develop a code of silence as a way of communication in order to find the best strategy. When analyzing real world cases, it becomes important to be able to factor in the lengths/”rounds” when trying to find the Nash Equilibria. Applying this concept to game theory, the article delves into justifying the play chosen by the Seahawks coach during one of the last plays in the 2015 Super Bowl.
During the 2015 Super Bowl, Pete Carroll made the seemingly outrageous move of having the Quarter Back, the player throwing the ball, attempt to make a pass for the completion of the run. While to most this would seem like a reasonable strategy, the fact that the Seahawks were 1 yard from the end-zone with time almost about to expire and 3 chances to get to the end-zone within the allotted game time (the Seahawks were most likely going to have the last possession of the ball making it a game-deciding possession) made this seem like an unreasonable plan; however, the article explains that this was not a mistake and there was solid reasoning behind this choice.
The last play of the game will basically have no signalling function, meaning neither of the parties cares about signalling to one another about the next play, therefore it is a safe assumption that the party with the ball will run it since it has the greatest percentage of success, especially at a small distance as 1 yard. So if the game only had 1 down left, it would be exactly like the Prisoner’s Dilemma, since it is the same as having the “one round.” The second-to-last play will basically have no signalling effect, since after the first round, the last play will, as explained before, be a running play. The second-to-last play will therefore also most likely be a running play unless the team with the ball gambled on getting lucky, which would be a near impossibility since it is the last play of the Super Bowl. So, now, three chances, the position the Seahawks were in, is a much more different than the other two considerations because there is leeway for a signalling function. This was the Seahawks’ last chance to make an unpredictable strategy, since a passing play on the first of the three chances would make the other party second-guess the next play. The plan for strategy for making a pass play on the first chance already has a low chance of being chosen, but that low percentage makes the next play more unpredictable (by making the percentage of doing another pass-play greater than zero) since the attempt of having a passing play in any of the three chances is so unpredictable. This concept that the length of the game/chances can effect the game theory/ predictability of strategies of the game, according to the article, is enough to justify the passing play strategy. However, in the end, the pass of intercepted during the first chance, and the game was not played out, leaving this theory without application in the 2015 Super Bowl, and the Seahawks fans angry at the faulty strategy of coach Carroll.
link:https://www.economist.com/game-theory/2015/02/03/threes-a-charm