Your stability argument is persuasive, but “a school’s dominant strategy is to outbid rivals” is not quite a game-theoretic certainty. Schools value winning, but they also face budget constraints, uncertain returns, and diminishing gains from each additional recruit. Unrestricted bidding can create an arms race; it doesn’t prove that every school will spend without limit or that a cap is the only stable solution.
A fixed stipend is stable only if it can be enforced and is set through a legitimate process. A school- or league-imposed cap can suppress athletes’ bargaining power while leaving spending on coaches, facilities, and recruiting largely untouched. And if outside NIL payments remain available, a cap on direct stipends may shift the bidding rather than stop it.
The strongest version of your proposal is therefore not simply “cap payments,” but a collectively negotiated, transparent compensation system: define what counts as compensation, apply rules consistently, and provide meaningful athlete representation. A cap or salary pool could be part of that bargain, alongside minimum payments and protections against schools using the cap to keep all the gains. That may be more stable than open-ended bidding—but stability alone doesn’t establish fairness.