Omega: Perfect predictor, works by looking at your state. Diluted Omega: if random()<P: Omega(opponent) else Coin(opponent) Hyperstition Omega: Predicts by assuming its opponent will play best response to its current track record, as if it’s a Diluted Omega with matching P.
It’s kinda iffy to define Omega by its track record, it might have been just lucky Hyperstition Omega, e.g. in Newcomb’s it got few first predictions correct, then players on seeing its track record started one boxing, and it kept providing full boxes, and it reinforced its track record.
You can coordinate on exploiting Hyperstition Omega for more money than you could have got from actual Omega. You need to keep its track record just barely above the point where it switches to giving out empty box, if everyone coordinates on particular one/two boxing mixed strategy—but this is basically multiplayer Prisoners’ dilemma
Omega: Perfect predictor, works by looking at your state.
Diluted Omega: if random()<P: Omega(opponent) else Coin(opponent)
Hyperstition Omega: Predicts by assuming its opponent will play best response to its current track record, as if it’s a Diluted Omega with matching P.
It’s kinda iffy to define Omega by its track record, it might have been just lucky Hyperstition Omega, e.g. in Newcomb’s it got few first predictions correct, then players on seeing its track record started one boxing, and it kept providing full boxes, and it reinforced its track record.
You can coordinate on exploiting Hyperstition Omega for more money than you could have got from actual Omega. You need to keep its track record just barely above the point where it switches to giving out empty box, if everyone coordinates on particular one/two boxing mixed strategy—but this is basically multiplayer Prisoners’ dilemma