Serious take
CDT might work
Basically because of the bellman fact that
the option
1 utilon, and play a game with EV 1 utilon are the same.
So working out the bellman equations
If each decision changes the game you are playing
This will get integrated.
In any case where somebody is actually making decisions based on your decision theory
The actions you take in previous games might also have the result
Restart from position x with a new game based on what they have simulated to do
The hard part is figuring out binding.
Serious take
CDT might work
Basically because of the bellman fact that
the option
1 utilon, and play a game with EV 1 utilon are the same.
So working out the bellman equations
If each decision changes the game you are playing
This will get integrated.
In any case where somebody is actually making decisions based on your decision theory
The actions you take in previous games might also have the result
Restart from position x with a new game based on what they have simulated to do
The hard part is figuring out binding.