I'll post this here, because it's somewhat related. I've asked a few people that two box in Newcomb's problem what they would do in a variation of the problem. Instead of deciding to one box or two box, you are asked to write a program that will one box or two box, and Omega is given access to the source code before filling the boxes. When phrased like this, the few two boxers I asked said they would write the program to one box.

Note that assuming that the people in question are emulating CDT agents this is precisely what we would expect (and CDT is the most plausible hypothesis for the kind of decision algorithm they are emulating). Similarly, if a (sane) CDT agent exists at time T with the capability to (relatively cheaply) self modify it will immediately alter itself into "CDT++". Roughly speaking it will end up as an agent that operates similarly to TDT for the purpose of influencing decisions that occur after time T but similarly to CDT for the purpose of influencing decisions that occur before time T. CDT is not in a stable equilibrium according to its own decision algorithm!