One could reframe this so that defecting on the 100th step kills 100 million, as that is what you’re going to lose over all the rounds.
If the other agent knows how you will reason, the games look like
C/C * 100 = 200 Million lives+paperclips D/D * 100 = 100 Million lives+paperclips
The difference between these is 100Million, which is how much you’re going to be penalized for reliably defecting on the last round.
One could reframe this so that defecting on the 100th step kills 100 million, as that is what you’re going to lose over all the rounds.
If the other agent knows how you will reason, the games look like
C/C * 100 = 200 Million lives+paperclips D/D * 100 = 100 Million lives+paperclips
The difference between these is 100Million, which is how much you’re going to be penalized for reliably defecting on the last round.