The folklore that was passed down to me in grad school was that philosophers regarded Savage-style evidential decision theory as more or less a done deal until Newcomb in 1968. Thereafter, the evidential vs causal vs something else debate shows no signs of ending. What's the history in econ?
In econ no one has ever heard of evidential decision theory. Our folklore includes examples like my test problem elsewhere in the thread as illustrations of canons of model construction. Newcomb is mostly treated as a curiosity, since every theory we have has at least one counter example.
When people do treat Newcomb, they follow a strategy like the one I mentioned. Gilboa assumes that the predictor really can respond to my choice (maybe he’s a carny with a false bottom box)—that model recommends one-box. Dekel and Gul assume the predictor cannot respond to my actual choice.
Their state space validates the dominance argument and recommends two boxing. They also analyze the perfect prediction clause game-theoretically—the predictor is always right in equilibrium. They argue that assuming their predictor is correct if I deviate leads to a contradiction