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I don't think human behaviour and relationships are reducible to economics like that.
It seems like you're pretty much starting from the axiom that economic calculus has to be at the bottom of everything, and any behaviour that isn't explicitly game theory has to be an abstraction/higher level implementation of it.
That's just not how people work.
Evolution didn't happen bottom up from an economics textbook. Behaviour that results in "winning" outcomes gets propagated. You can examine those from the perspective of economic theory, but economic theory isn't the origin.
There doesn't need to be a hidden "econ 101" subroutine that obfuscates itself.
The much simpler explanation is that unconditional relationships have been adaptive and beneficial, if not for the individual then for the group, just as being deceptive about ones commitment to others can be a competitive advantage.
Something tells me that the selective pressure to keep "the tribe" alive has been a much more fundamental factor for the evolution of human social behaviour than the pressure to attain a resource advantage over our peers.
Therefore, I think genuinely "unconditional" relationships existing is the much more likely explanation.
("Unconditional" with the exception of the other side defecting in substantial ways. These relationships can be broken, but only if the underlying belief gets falsified).