Though I got downvoted quite a bit I thought it was an interesting question about the relationship between Objectivism and Game Theory and found a couple links. Keep in mind that these are from the Atlas institute so they are surely very biased opinions, but I thought it was interesting to see the defense of Objectivism in regards to game theory questions.
It's a fair question, but the whole point of Axelrod /The Selfish Gene / Cooperative Games is to call out how much a game theory approach would support strategies which are anti-Objectivist. Where contributing to the commons, investing in public good, cooperating, radically grows the pie to the point where it's in everyone's self interest to cooperate.
Basically, times in life where it's a 'positive sum' as opposed to 'zero-sum' game.
Non-zero by Robert Wright, is probably the best synthesis on this topic.
Sorry for the downvote. It was a good question, but I did not want to encourage a link between game theory and objectivism to the casual observer because I seem them as complete opposites. Objectivism is, at best, short-sighted - screwing over the people around you because it is convenient in the moment and becoming indignant when the folks that were mistreated no longer want to be your friend. (At worst it is justification for people that enjoy inflicting cruelty on others.) Game theory can demonstrate how to be truly selfish, it is in our best interest to be kind, thoughtful, and good communicators and to cultivate strong and healthy relationships.
I actually think there are some parallels when you listen to Rand herself talk about cooperation in a selfish framework: https://youtu.be/CoAKer8lfds
I think she outlines cooperation as an intrinsic result when people are acting within their own self interests which I think was why I originally saw the relationship.
One about game theory and its relation to Objectivism: https://www.atlassociety.org/post/game-theory-and-objectivis...
And another about the Prisoners Dilemma specifically and which touches on the Nash equilibria: https://www.atlassociety.org/post/prisoners-dilemma
And for people like me who are interested in the relationships between the two, here are some opinions of people from quora: https://www.quora.com/How-does-Objectivism-view-the-Nash-equ...