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There has been a huge mathematical, philosophical, and sociological outburst of theory and research in regards to Game Theory since it was founded. I'm not up on all of it, but I try to stay up on this side of it.
I read a lot on it as well. The best way I read about of looking at religion through a game theory lens goes like this:
1) Religion requires its adherents to act is an irrational manner - specifically through the form of forgiving those who have trespassed against us. It is not rational to forgive someone who has stolen from you or assaulted you as they will likely do so again to you or others in the future.
2) But what does a purely rational word with no forgiveness look like? A very tribal and brutal one where the social order collapses. Even on a micro level, the inability to forgive would lead to a collapse in social or friend based or marital bonds
3) So in engaging in forgiveness, we build a more stable and mutually beneficial society that advances your long-term self interest compared to the alternative. That is essentially the game theory optimal outcome being achieved by short-changing yourself..
This line of thought was then enhanced through the in group and out group line of thinking in sociology. We tend to engage in forgiveness for members of our in-group while being much more hostile to out groups.
I think this helps explain the moral cognitive dissonance on display in many religious, secular, or cultural groups that engage in forgiveness in one setting but then take more hostile stances towards outgroups, whether that be westerners deriding Muslim culture and vice versa, U.S. Citizens being hostile to illegal immigrants or just the garden variety hatred between "Evil Godless Stupid Ugly Libs" and "Dirty, Uneducated, Volatile, Redneck Maga Boomer Idiots"