I think the clearest and simplest version of Problem 1 is where Omega chooses to simulate a CDT agent with .5 probability and a TDT agent with .5 probability. Let’s say that Value-B is $1000000, as is traditional, and Value-A is $1000. TDT will one-box for an expected value of $500500 (as opposed to $1000 if it two-boxes), and CDT will always two-box, and receive an expected $501000. Both TDT and CDT have an equal chance of playing against each other in this version, and an equal chance of playing against themselves, and yet CDT still outperforms. It seems TDT suffers for CDT’s irrationality, and CDT benefits from TDT’s rationality. Very troubling.
EDIT: (I will note, though, that a TDT agent still can’t do any better by two-boxing—only make CDT do worse).
I think the clearest and simplest version of Problem 1 is where Omega chooses to simulate a CDT agent with .5 probability and a TDT agent with .5 probability. Let’s say that Value-B is $1000000, as is traditional, and Value-A is $1000. TDT will one-box for an expected value of $500500 (as opposed to $1000 if it two-boxes), and CDT will always two-box, and receive an expected $501000. Both TDT and CDT have an equal chance of playing against each other in this version, and an equal chance of playing against themselves, and yet CDT still outperforms. It seems TDT suffers for CDT’s irrationality, and CDT benefits from TDT’s rationality. Very troubling.
EDIT: (I will note, though, that a TDT agent still can’t do any better by two-boxing—only make CDT do worse).