The Game Theory behind a Six Overtime Thriller
This past weekend Cornell’s Sprint football team opened there season with a win, in a game that would turn out to be one for the ages. After waiting through a ninety minute lightning delay the Big Red found themselves in a dog fight with the Quakers of UPenn. As the clock wound down marking the end of regulation the teams were deadlocked at 21 and overtime was impending. Through six periods of overtime the teams battle to put points on the board and then quell their opponent’s rebuttal. With a lot of hard work, and just as many great play calls, the Big Red won 42-34.
Game theory is ever present in the game of football. Before each play teams make a decision on what to do based on their offensive or defensive strategies, and what they believe the defense will do. The outcomes of those decisions then shape how the game unfolds.Under NCAA collegiate rules each team gets a possession in overtime, and thus a chance to score. If the team that starts with the ball scores than they must stop the opposing offense from matching the number of points that they scored in order to win. The offensive team can choose to pass or run the ball and the defense could have chosen to defend the pass or defend the run (after the teams switch possession the payoffs remain the same but interchange between offensive and defensive strategies). Due to the fact that both the offense and defense have two strategies, this game can be modeled similarly to the prisoner’s dilemma.
The payoffs table would look like this:
Defense
Defend Pass Defend Run
Pass 0,0 12,-12
Offense
Run 5,-5 1,-1
If the defense stops the offense four times in a row by choosing the right defensive strategy, then they regain possession for their offense, and they can then choose to either pass or run in their attempt to score. In this situation there is no pure strategy Nash equilibrium, because in no instance is one teams best possible response paired with the best possible response of the other team. Due to the fact that UPenn was not able to choose the right strategies to stop, while Cornell did choose the correct strategies, the Big Red were able to win the game.
Source: http://cornellbigred.com/news/2012/9/14/SPRINT_0914122403.aspx
-SprintFootball37
The sprint football analogy was a cool way to demonstrate the “coordination game” that occurs when there are not any pure strategy nash equilibriums. It would be cool to determine what the mixed nash equilibrium is for this game and compare it to the actions of the teams. It appears to me that the payoffs for when the offense runs will always result in the offensive team making progress. Would this be a dominant strategy for the offense?