On an extremely similar note, as I've argued here, I'm pretty sure that AIXI two-boxes on Newcomb's problem.

Basically my argument is that AIXI can fairly trivially work out whether the box is full or empty, and hence it two-boxes due to causal assumptions implicit in the AIXI algorithm. Moreover, that line of reasoning is very easy for Omega to come across, and so Omega predicts two-boxing and the box ends up being empty, and then AIXI takes two boxes and ends up with $1000.