Assuming that the space of possible agents is large enough:
For each individual version of a TDT agent, the best way is to two-box. The advantage of TDT is the possibility to improve the expected value for a whole range of agents (including cooperation with other TDT agents in the prisoners dilemma). CDT agents happen to profit from that, and they profit even more than TDT agents. Does TDT maximize the expected value for the whole distribution of agents? In that case, it is still optimal in that respect.
Problem 2 is sensitive to changes of arbitrary size: Assume that the space of TDT agents takes one box with probability 10%+epsilon and some other with 10%-epsilon. While the expectation value is the same within O(epsilon), the money is now in some other box and CDT would have to calculate that with the same precision. Apart from the experimental issue, I think this gives some theoretical challenges as well.
Assuming that the space of possible agents is large enough: For each individual version of a TDT agent, the best way is to two-box. The advantage of TDT is the possibility to improve the expected value for a whole range of agents (including cooperation with other TDT agents in the prisoners dilemma). CDT agents happen to profit from that, and they profit even more than TDT agents. Does TDT maximize the expected value for the whole distribution of agents? In that case, it is still optimal in that respect.
Problem 2 is sensitive to changes of arbitrary size: Assume that the space of TDT agents takes one box with probability 10%+epsilon and some other with 10%-epsilon. While the expectation value is the same within O(epsilon), the money is now in some other box and CDT would have to calculate that with the same precision. Apart from the experimental issue, I think this gives some theoretical challenges as well.