A “naturalistic” approach to game theory is one in which game theory is an application of decision theory (not an extension) -- there should be no special reasoning which applies only to other agents.
But game theory doesn’t require such special reasoning! It doesn’t care how players reason. They might not reason at all, like the three mating variants of the side-blotched lizard. And when they do reason, game theory still shows they can’t reason their way out of a situation unilaterally, no matter if their decision theory is “naturalistic” or not. So I think of game theory as an upper bound on all possible decision theories, not an application of some future decision theory.
But game theory doesn’t require such special reasoning! It doesn’t care how players reason. They might not reason at all, like the three mating variants of the side-blotched lizard. And when they do reason, game theory still shows they can’t reason their way out of a situation unilaterally, no matter if their decision theory is “naturalistic” or not. So I think of game theory as an upper bound on all possible decision theories, not an application of some future decision theory.