I don't think there's just one successful game theory strategy.

"Do unto others as you would have them do unto you."
is a kind of a planning-ahead strategy if you believe that others
are going to use "tit for tat". Maybe?

And besides, I'm talking about a strategy that is beneficial to the group
(and to group members indirectly thereby. Not a strategy that is most
beneficial on average to the individual at each encounter.

Frank wrote:

Actually, the successful game theory strategy is "tit for tat"

which would be quivalent to: "an eye for an eye"

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