"Game theory" (related more to your point about the Red Queen than the OP about actual games!😉) has advanced quite a bit since it's earlier days. The prisoner's dilemma thought experiment, for instance, was shown to be extremely naive and simplistic since it presumes single isolated incidents each and every single time - complete independence of all events from one another: a situation that has never once been true in the entire existence of the whole universe. So spherical chickens sliding on frictionless surfaces and whatnot, allowing them to continue literally forever, once you remove anything stopping them, i.e. friction, from consideration. i.e. any claim resulting from such a naive thought experiment has zero bearing on actual real life, which has, you know, friction present in it, and therefore e.g. motion cannot continue forever but will eventually stop.

The very next time that the prisoner dilemma scenario gets tried though, everyone knows the results of the former one - so a traitor selling out others for their own gain is known to be such. Meanwhile, cooperative networks are formed that vastly beat out any such singlemindedly selfish agenda - much like happens in actual prisons. Therefore, even the most selfish person, if they also possess even the slightest hint of intelligence, will not betray literally everyone they encounter every single time, but instead will form alliances ASAP. i.e. they will consider the needs of others, even if only purely as a means to the end of meeting their own selfishly.

Enlightened selfishness leading to altruistic behavior? Researchers performed extensive simulations and... YES, that is what came out of them!?! It only seems counterintuitive if you believed the hype spread by culture earlier that people are isolated unto themselves, entirely distinct from everything that goes on all around them. You know, naïveté in early psychology, necessitated perhaps by needing to lay down some foundational groundwork principles, yet attesting then to the fact that the entire field was too newly formed to be able to clean much in the way of actionable results from it - and in fact could even be lead astray, unawares i.e. it was too soon to pay attention to it (and it may yet still, but the beauty of science is that it will always remain thus, ever advancing and improving upon itself:-). Anyway, the golden rule of treating others as you want to be treated was found to be literally a mathematical principle of game theory... so long as there are multiple experiments in a row, and the results are observable by others.

Your reputation proceeds you, and then others respond in kind. This much is true regardless of personal preference. Given that then, the best strategies often are to assume reciprocity in advance, and then immediately take it away if ever betrayed (no need to be a doormat, that's just as naive and equally bad as always betraying everyone else first, in fact slightly more so since the latter will win at least the very first time even if never subsequently).

Anyway I don't know how precisely to apply any of this to help solve the situation with actual games - except that a problem needs to first be diagnosed prior to a treatment being deployed.