Mixed Nash Equilibrium in Football
This article about the way the Seahawks use their top-flight cornerback, Richard Sherman, reminded me of the game theory concepts we’ve discussed in lecture.
Basically, what the Seahawks do is keep Sherman on one side of the field for the entire game, instead of having him follow the other team’s best receiver in coverage. He did this for the week 1 game against my favorite team, the Packers, and spent all game covering our third best receiver (Jarrett Boykin) and was never thrown at. I believe this demonstrates a failure of at least one team to properly embrace the core idea of the mixed Nash equilibrium. While the point could be argued that having Sherman lock down one side of the field is a dominant strategy, if that is not the case then the Seahawks would be better off having him sometimes swap sides to follow a certain receiver. At the very least, this would ensure that other teams (perhaps ones better than my Packers this year…) could not exploit the fact that they know what at least part of the coverage they will be facing will look like. What isn’t debatable in my mind is that you have to throw at Sherman a couple times. By restricting your own possible strategies so severely, it becomes much easier for the defense to predict and exploit the offensive strategy. As we have calculated more rigorously in homework and in lecture, you need to undertake strategies with reduced payoff in some proportion to reach the mixed equilibrium. I think NFL coaches are very conservative with regards to this sort of approach, and yet constantly reference it indirectly with “staying with the run game” even when behind to keep the defense “on its toes”. In competitive games like football, it’s important to preserve unpredictability, and I think the Packers and Seahawks might both have room for improvement in that regard.