The fundamental flaw in applying game theory to biology is to constrain the possible outcomes when unfairness is detected. In game theory, all you can do is change your strategy for the next round; in reality, we have multiple punishments to bring to bear, such as refusing to play, public shaming, fines, imprisonment, killing, etc.
Game theory is only an "ok" model of cooperation/competition in real life.
Also worth mentioning that while the classic game theory approach is to calculate the optimum strategy, there's also evolutionary game theory, which looks at what strategies could actually be found by an evolutionary process. They tend to be the same, but not always.
"Choosing among a set of games" seems to me to be just a bigger game. "Known histories" can include any iterated game, which is a basic part of game theory. It's also studied a lot in the context of poker, where the challenge is that if you deviate from the game-theory optimal strategy to better exploit your opponent, you open yourself up to exploitation.
For the most part, people cooperate when the outcome of cooperating puts them at a better place. In the same way everyone is unique but they copy proven paths to achieve certain ends or move to certain stages where they can eventually break off and get ahead personally. In the same way groups suck but we all live better that there are other people.
All of life is similar, self-interested for survival, but they want a place of their own and territory, eventually.
Historicaly the countries that were on the "low profit" end of international trade and followed the comparative advantage theory advice - lost (see Argentina), and the countries that contrary to the theory tried to move to more complex products/services and bigger profits - won (see Germany, USA), even if they had to abandon their comparative advantages, suffer international trade restrictions, etc to get there.
It turns out industrialization not only makes you better at producing machines - it also makes you better at producing food, and almost everything else. Meanwhile producing food just produces food.
I find it fascinating that twisting the parameters changes the outcome. Thinking about our social world, for example fraud in finance, perhaps there is something to be learned about the way the rules of society should be set up to eliminate cheating.