I just figured out why Newcomb’s problem feels “slippery” when we try to describe it as a two-player game. If we treat the predictor as a player with some payoffs, then the strategy pair {two-box, predict two-boxing} will be a Nash equilibrium, because each strategy is the best response to the other. That’s true no matter which payoff matrix we choose for the predictor, as long as correct predictions lead to higher payoffs.
I don’t see how two-boxing is a Nash equilibrium. Are you saying you should two-box in a transparent Newcomb’s problem if Omega has predicted you will two-box? Isn’t this pretty much analogous to counterfactual mugging, where UDT says we should one-box?
Sorry, I wrote some nonsense in another comment and then deleted it. I guess the point is that UDT (which I agree with) recommends non-equilibrium behavior in this case.
I just figured out why Newcomb’s problem feels “slippery” when we try to describe it as a two-player game. If we treat the predictor as a player with some payoffs, then the strategy pair {two-box, predict two-boxing} will be a Nash equilibrium, because each strategy is the best response to the other. That’s true no matter which payoff matrix we choose for the predictor, as long as correct predictions lead to higher payoffs.
I don’t see how two-boxing is a Nash equilibrium. Are you saying you should two-box in a transparent Newcomb’s problem if Omega has predicted you will two-box? Isn’t this pretty much analogous to counterfactual mugging, where UDT says we should one-box?
Sorry, I wrote some nonsense in another comment and then deleted it. I guess the point is that UDT (which I agree with) recommends non-equilibrium behavior in this case.