-”The main question is: In the counter-factual scenario in which TDT recommends action X to agent A , what does would another agent B do?”
This is actually not the main issue. If you fix an algorithm X for agent A to use, then the question “what would agent B do if he is using TDT and knows that agent A is using algorithm X?” has a well-defined answer, say f(X). The question “what would agent A do if she knows that whatever algorithm X she uses, agent B will use counter-algorithm f(X)” then also has a well-defined answer, say Z. So you could define “the result of TDT agents A and B playing against each other” to be where A plays Z and B plays f(Z). The problem is that this setup is not symmetric, and would yield a different result if we switched the order of A and B.
-”In a blackmail scenario it’s not so obvious, but I do think there is a certain symmetry between rejecting all blackmail and sending all blackmail.”
The symmetry argument only works when you have exact symmetry, though. To recall, the argument is that by controlling the output of the TDT algorithm in player A’s position, you are also by logical necessity controlling the output in player B’s position, hence TDT can act as though it controls player B’s action. If there is even the slighest difference between player A and player B then there is no logical necessity and the argument doesn’t work. For example, in a prisoner’s dilemma where the payoffs are not quite symmetric, TDT says nothing.
-”So I no longer believe the claim that TDT agents simply avoid all negative-sum trades.”
I agree with you, but I think that’s because TDT is actually undefined in scenarios where negative-sum trading might occur.
-”The main question is: In the counter-factual scenario in which TDT recommends action X to agent A , what does would another agent B do?”
This is actually not the main issue. If you fix an algorithm X for agent A to use, then the question “what would agent B do if he is using TDT and knows that agent A is using algorithm X?” has a well-defined answer, say f(X). The question “what would agent A do if she knows that whatever algorithm X she uses, agent B will use counter-algorithm f(X)” then also has a well-defined answer, say Z. So you could define “the result of TDT agents A and B playing against each other” to be where A plays Z and B plays f(Z). The problem is that this setup is not symmetric, and would yield a different result if we switched the order of A and B.
-”In a blackmail scenario it’s not so obvious, but I do think there is a certain symmetry between rejecting all blackmail and sending all blackmail.”
The symmetry argument only works when you have exact symmetry, though. To recall, the argument is that by controlling the output of the TDT algorithm in player A’s position, you are also by logical necessity controlling the output in player B’s position, hence TDT can act as though it controls player B’s action. If there is even the slighest difference between player A and player B then there is no logical necessity and the argument doesn’t work. For example, in a prisoner’s dilemma where the payoffs are not quite symmetric, TDT says nothing.
-”So I no longer believe the claim that TDT agents simply avoid all negative-sum trades.”
I agree with you, but I think that’s because TDT is actually undefined in scenarios where negative-sum trading might occur.