"...if moral behaviour is consistent with game theory, that might be because game theory and the just-so stories of evolutionary psychology are unfalsifiable and tautological. "
Don't all mathematical proofs prove tautologies? On a plane, the square on the hypotenuse MUST be equal to the sum of the squares on the other two sides. That fact is inherent in the nature of a plane, as defined by Euclid's axioms. Axioms are unfalsifiable. Game theory simply proves a tautology about decision spaces in which the unfalsifiable axioms are the pay-offs. What if Euclid had not posited the parallel line thing? His plane geometry wouldn't be terribly useful, because his "plane" wouldn't map to anything we want to measure. GI, GO.
Likewise, people can disagree about the choice of axioms for a decision space. Values vary. and factual information is incomplete. Not only don't we know how to make it rain tomorrow, we can't even agree on whether we WANT it to rain tomorrow. But if we agree that we want it to rain, very elementary game theory suggests that research into causing rain is a better strategy than doing nothing. Is that a tautology? Does it matter? Complicating the problem and using less obvious elements of game theory does not change anything except the risk of garbage going in and, therefore, coming out.
I sometimes have ideas that seem clever to me but which I know are not really novel and can, with very little effort, be found elsewhere on the 'Net. So, taken with the idea of a geometry of a decision space, I looked it up and found this: https://www.researchgate.net/publication/228624144_The_geometry_of_decision_theory The math is beyond me, but I'm heartened that someone who, unlike me, actually purports to know what he's talking about has explored the idea of geometry and decision theory. That just leaves the leap from morality to decision theory. Once again, the Google ex machina saves save day.
I won't recommend these articles, as I have not read them (did I mention being out of gas?) and even if I did read them, the odds are pretty good that I would still have no idea whether they are any good. OTOH, they MAY support my speculations or even demonstrate them to have some merit. If not, then not.
Maybe I should recap my position.
Hobbes describes a plus-sum game where the payoff is life for "man" (whatever that means) that is not solitary, poor, etc. Hobbes's solution is coordination, aka civilization, with "Leviathan" as coordinator. I am suggesting that morality does some of the coordinating work, with God or ancestors or custom or reason being the "source" of morality. While it is quite easy for Hobbes to describe what a bad outcome looks like, it is harder for us to describe what the best outcome looks like, because people don't agree on what is best. Game theory confirms only that man has the opportunity to use rules to make things better, because coordination produces plus-sum results in iterated, multi-player Prisoners' Dilemma games, e.g., life. Moral philosophy exists to find those rules, both by identifying the best outcome and identifying the best way to achieve it.
Libertarians merely assert, in my view, a presumption against rules with respect to any particular activity, combining the claim that they own their bodies and outputs with some vague constraint on doing (undefined) harm to others. In my view, "harm" is whatever society decides it is, and the self-ownership thing is just noise because the no-harm rule trumps it. In other words, libertarians are morons. And I say this as someone who entertains the presumption that there should only be rules where the reduction of harm can be demonstrated, recognizing that "harm" is always politically defined.