It’s the biggest moment in your N.F.L. coaching career: 26 seconds remain in the Super Bowl, your team is 4 points behind, you have the ball just one yard short of the end zone, it’s second down, and your team has arguably the N.F.L.’s best running back. What’s your call? Run or pass?

Here’s what I would do: Call a game theorist, someone who specializes in the branch of economics that analyzes strategic interactions. Game theory is the tool used to understand how global superpowers respond to each other, how large companies compete with each other and how grandmasters play chess. It also describes the strategic tussle between Bill Belichick, the coach of the New England Patriots, and Pete Carroll, the coach of the Seattle Seahawks, who found themselves facing difficult decisions in the final seconds of Sunday’s Super Bowl.

The key insight of game theory for an N.F.L. coach is that when you think about what choice you should make, you need to also consider the response from the opposing coach, understanding that he is also thinking strategically. This line of thinking suggests that you should not necessarily call a run play, even if you’re blessed with a great running back. Likewise, it’s not clear that you should definitely pass. Rather, your choice should be somewhat random — a choice that game theorists call a “mixed strategy.”

The logic is that if you always choose to run in this situation, then you make the opposing coach’s job too easy, as he will set a defensive formation aimed at stopping your running back. Forget guarding the receivers, Belichick would respond by piling players between Marshawn Lynch and the end zone. As great as Lynch is, even he would find it difficult to run over a stacked defense that was waiting for him. Likewise, if the Seahawks would always decide to pass in this situation, there would be little need for the Patriots to guard against the run, and so their defense could double-team the eligible receivers.