Very raw comment follows, I hope others can make something of it.
In short, yeah. The best response to TDT isn’t necessarily TDT. So for TDT to constitute a “Nash equilibrium in algorithms” against itself, it needs to include precautions against exploiters, e.g. precommit to defecting against the defector in your game even though it looks suboptimal. We haven’t yet solved this problem in general. My current best idea (suggested by user Perplexed) is to use Nash’s 1953 paper to pick a fair outcome and disagreement point, then play accordingly: demand your fair share and punish at all costs if you don’t get it. In your game this would lead to the outcome 2⁄2. But this has the big drawback that “other players” are treated differently from static parts of the world-program. It may be fixable but I don’t yet know how.
Also Wei Dai’s workshop post on Jun 15 about “the stupid winner paradox” seems to be relevant, but I can’t copy-paste the whole resulting email exchange here. Maybe ask Wei to repost it to LW?
Very raw comment follows, I hope others can make something of it.
In short, yeah. The best response to TDT isn’t necessarily TDT. So for TDT to constitute a “Nash equilibrium in algorithms” against itself, it needs to include precautions against exploiters, e.g. precommit to defecting against the defector in your game even though it looks suboptimal. We haven’t yet solved this problem in general. My current best idea (suggested by user Perplexed) is to use Nash’s 1953 paper to pick a fair outcome and disagreement point, then play accordingly: demand your fair share and punish at all costs if you don’t get it. In your game this would lead to the outcome 2⁄2. But this has the big drawback that “other players” are treated differently from static parts of the world-program. It may be fixable but I don’t yet know how.
Also Wei Dai’s workshop post on Jun 15 about “the stupid winner paradox” seems to be relevant, but I can’t copy-paste the whole resulting email exchange here. Maybe ask Wei to repost it to LW?