I would one-box if I had the one-boxing gene, and two-box if I had the two-boxing gene. I don't know what decision-making theory I'm using, because the problem statement didn't specify how the gene works.
I don't really see the point of asking people with neither gene what they'd do.
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This is no different from responding to the original Newcomb's by saying "I would one-box if Omega put the million, and two-box if he didn't."
Both in the original Newcomb's problem and in this one you can use any decision theory you like.
There is a difference - with the gene case, there is a causal pathway via brain chemistry or whatnot from the gene to the decision. In the original Newcomb problem, omega's prediction does not cause the decision.