The simulated TDT agent is not aware that it won’t receive a reward, and therefore it does not work.
This raises an interesting problem, actually. Omega could pose the following question:
Here are two boxes, A and B; you may choose either box, or take both. You are in one of two states of nature, with equal probability: one possibility is that you’re in a simulation, in which case you will receive no reward, no matter what you choose. The other possibility is that a simulation of this problem was presented to an agent running TDT. I won’t tell you what the agent decided, but I will tell you that if the agent two-boxed then I put nothing in Box B, whereas if the agent one-boxed then I put $1 million in Box B. Regardless of how the simulated agent decided, I put $1000 in Box A. Now please make your choice.
The solution for a TDT agent seems to be choosing box B, but there may be similar games where it makes sense to run a mixed strategy. I don’t think that it makes much sense to rule out the possibility of running mixed strategies across simulations, because in most models of credible precommitment the other players do not have this kind of foresight (although Omega possibly does).
And yes, it is still the case that a CDT agent can outperform TDT, as long as the TDT agent knows that if she is in a simulation, her choice will influence a real game played by a TDT, with some probability. Nevertheless, as the probability of “leaking” to CDT increases, it does become more profitable (AIUI) for TDT to two-box with low probability.
This raises an interesting problem, actually. Omega could pose the following question:
The solution for a TDT agent seems to be choosing box B, but there may be similar games where it makes sense to run a mixed strategy. I don’t think that it makes much sense to rule out the possibility of running mixed strategies across simulations, because in most models of credible precommitment the other players do not have this kind of foresight (although Omega possibly does).
And yes, it is still the case that a CDT agent can outperform TDT, as long as the TDT agent knows that if she is in a simulation, her choice will influence a real game played by a TDT, with some probability. Nevertheless, as the probability of “leaking” to CDT increases, it does become more profitable (AIUI) for TDT to two-box with low probability.