Decision-theoretic variant: build an agent that incorporates a quantum random number generator, such that with some small probability it will output a random action. Then have the agent calculate how much expected utility each action would imply if it were chosen because of the random number generator, and output the best one.

Unless I'm missing something, this agent doesn't play very well in Newcomblike problems, but seems to be a good enough formalization of CDT. I cannot define it as formally as I'd like, though, because how do you write a computer program that refers to a specific quantum event in the outside world?