Since the late 19th century, American universities have known that when their football teams win, their alumni donations increase. Universities need those donations to support their financial goals of long-term sustainability and their ethical goals of supporting basic research and expanding access to low-income applicants.

The problem is, football games are zero-sum, and that means that American universities are in a situation that is familiar to every student of game theory, evolutionary biology or IR: an arms race. It makes sense for Yale to improve its football team by 10 percent, to increase its chances of beating Harvard and cashing in on alumni donations — and it makes sense for Harvard to do the same. But when both universities do it, both are worse off because one university’s win is another’s loss. This goes for the whole NCAA, too. What makes sense for each university is costly for the system as a whole.

Even worse, we’ve all converged on a particularly problematic sport. Every week we read new research about the elevated risks of dementia, depression, suicide and attention deficits among football players who have suffered repeated concussions or even sub-concussive hits. Every week, we read a new story about a student who lost months of sleep or productive studying after a dizzying tackle. And there’s probably a lot more damage than we’re even measuring.

It’s perverse for institutions of higher learning to send unpaid student athletes onto the field to get concussed for their own fundraising purposes. It’s doubly perverse that elementary school and middle school kids do the same, inspired partly by the images of collegiate athletic glory on TV or by the prospect of a university admissions leg up.

Let me be clear: What I have said, and what I will propose, is not about the status or talent of Yale’s football players. The Yale footballers I’ve known have struck me as, if anything, even more accomplished than the typical Yalie. This call for reform is not about status and who deserves to be a Yalie.

Rather, this is about policy, young peoples’ brain health, university fundraising and sports governance. It’s about structuring rules and institutions in a way that is good for all of us.

Here’s what we should do: Yale and Harvard administrators should meet this year and agree to cancel The Game for 2014.

Instead, we’ll have a Yale-Harvard regatta, with men’s and women’s races on the Charles River the weekend before Thanksgiving. In 2015, The Regatta will come back to the Quinnipiac River. Yale and Harvard should legally commit to two constraints in advance: Both schools will field boats that are at least 50 percent walk-ons; both schools will limit total practice and competition time to 12 hours per week. (Basketball, baseball or cross-country could also substitute.)

That way, we will still get a game, a competition around which to enjoy our rivalry and to have an alumni weekend. But we won’t get an arms race in which university administrators feel pressured to give more slots to recruits, where athletic directors and coaches are pressured to push student athletes to more practice time — and where our schools’ champions get concussions. The 50 percent walk-on rule will give teams and coaches incentives to be attractive to non-recruited student athletes, which will expand access to the joys of athletics.

Yale and Harvard should not do this primarily for their own sakes but because they are models for all other American universities. As universities come under increasing pressure to control their costs and refocus on their core pedagogical mission, Yale and Harvard can show them how to collectively negotiate rules that will stop arms races and make cheaper and more accessible athletics programs.

Is football irreplaceable? I hope not — and I hope that Americans can learn to love another, safer sport. But if they can’t, here’s another relatively cheap idea: Yale and Harvard should offer a $1 million prize to the individual who proposes the best redesign of the rules of football that preserves its core attractions while nearly eliminating concussions. The prize-winning rules would have to receive the joint approval of the Yale and Harvard football teams and a panel composed of Yale and Harvard medical school faculty specializing in concussions.

Games are just man-made platforms for fair competition — so why not make a platform that doesn’t harm players? It’s the 21st century; maybe we could put sensors on gloves and jerseys that would register downs without tackles. With a few jiggles, the oldest football rivalry in history could start up again with Football 2.0. Someday, we could let our kids play the game without the fear that we’re dooming them to dementia or depression.

Does this proposal sound strange? I think a system of higher education that sacrifices students’ health to a fundraising tournament is even stranger.

Matthew Shaffer is a 2010 graduate of Davenport College and a former staff columnist for the News.