Game theory is a useful framework for this problem in the sense that almost any double-sided market can be trivially formulated into a game-theoretic framework. But viewing college admissions as a Nash equilibrium doesn't meaningfully clarify the problem.

That said, I generally agree with the article. America's elite private universities have almost always been about signalling over substance, an orientation that can be traced back to their origins as bastions of elite privilege. Our recent attempts at reform, via affirmative action and more recently, the SAT adversity score, have been nothing more than attempts to spread the benefits of signalling to new, heretofore underrepresented, groups.

The real solution, of course, is to tear this reputation market down. We need to work to remove the signalling benefits of so-called "elite" institutions, and in doing so, remove their stranglehold on access to a number of prestigious jobs and career paths.

How do we do this? I'm not sure, exactly. The radical solution is to nationalize all universities, redistribute their endowments more equitably, and enforce a singular admissions and educational process on all of them. This enforced uniformity would destroy "elite" signalling.

There are incremental steps to this, though. Implement new rules to force colleges to expand their enrollment to maintain non-profit status (and thus retain untaxed earnings from their endowments). Pour more money in flagship public universities to create strong alternatives to private education (i.e. make a UC Berkeley for every state). And so on. Reduce the distinctiveness of the elite privates, and their value as signalling institutions decreases.