Now consider what happens if the second player has more computing power than the first, so that it can perfectly simulate the first player and compute its move. After it finishes that computation and knows the first player’s move, the logical correlation between them disappears, because no uncertainty implies no correlation. So, given there’s no logical correlation, it ought to play D. The first player would have expected that, and also played D.
The first player’s move could depend on the second player’s, in which case the second player won’t get the answer is a closed form, the answer must be a function of the second player’s move...
But if the second player has more computational power, it can just keep simulating the first player until the first player runs out of clock cycles and has to output something.
I don’t understand your reply: exact simulation is brute force that isn’t a good idea. You can prove general statements about the behavior of programs on runs of unlimited or infinite length in finite time. But anyway, why would the second player provoke mutual defection?
But anyway, why would the second player provoke mutual defection?
In my formulation, it doesn’t have a choice. Whether or not it does exact simulation of the first player is determined by its “mathematical intuition subroutine”, which I treated as a black box. If that module does an exact simulation, then mutual defection is the result. So this also ties in with my lack of understanding regarding logical uncertainty. If we don’t treat the thing that reasons about logical uncertainty as a black box, what should we do?
ETA: Sometimes exact simulation clearly is appropriate, for example in rock-paper-scissors.
The first player’s move could depend on the second player’s, in which case the second player won’t get the answer is a closed form, the answer must be a function of the second player’s move...
But if the second player has more computational power, it can just keep simulating the first player until the first player runs out of clock cycles and has to output something.
I don’t understand your reply: exact simulation is brute force that isn’t a good idea. You can prove general statements about the behavior of programs on runs of unlimited or infinite length in finite time. But anyway, why would the second player provoke mutual defection?
In my formulation, it doesn’t have a choice. Whether or not it does exact simulation of the first player is determined by its “mathematical intuition subroutine”, which I treated as a black box. If that module does an exact simulation, then mutual defection is the result. So this also ties in with my lack of understanding regarding logical uncertainty. If we don’t treat the thing that reasons about logical uncertainty as a black box, what should we do?
ETA: Sometimes exact simulation clearly is appropriate, for example in rock-paper-scissors.