Consider the Prisoner’s Dilemma, modified so that one person moves first and the other person gets to observe their move before choosing.
Obviously the classically correct first move is to defect first. Thus the second player will never have to deal with a move of Cooperate.
Therefore if a move of Cooperate is made, the second player’s move is classically undefined (if one accepts the logic of this post). And yet, if both players play cooperate it’s better than (D,D), and so which move gets made first depends on the actions of the second player if Cooperate is played first. Therefore, this prisoner’s dilemma has no solution.
(I consider this to be a reductio).
Viewed this way, there’s an obvious relationship with the formal-agent problem of “I can prove what option is best, and I know I’ll take the best option—therefore, if I do something else all logical statements are conditioning on a falsehood, and so it’s true that I can get the best results by doing nothing.” The solution there is to not use logical conditioning inside the decision-making process like that, and instead use causal insertion
Similarly, we might never expect the second player in an ordered Prisoner’s Dilemma to have to deal with cooperation. But we can still talk about that counterfactual by declaring by fiat that the first move was cooperation and looking at the choices that result. Note the similarity between causal insertion and the trembling hand—almost like this trembling hand stuff works for a deeper reason. If our second PD player is an ordinary classical agent, they will choose Defect—problem resolved.
The game you present has an extra dimension, but upon learning that B or C were chosen (again, via causal surgery, not logical conditioning), a classical agent without additional information will just play the Nash equilibrium of the sub-game where only B or C are available—see JGWeissman’s comment for the correct numbers.
Consider the Prisoner’s Dilemma, modified so that one person moves first and the other person gets to observe their move before choosing.
Obviously the classically correct first move is to defect first. Thus the second player will never have to deal with a move of Cooperate.
Therefore if a move of Cooperate is made, the second player’s move is classically undefined (if one accepts the logic of this post). And yet, if both players play cooperate it’s better than (D,D), and so which move gets made first depends on the actions of the second player if Cooperate is played first. Therefore, this prisoner’s dilemma has no solution.
(I consider this to be a reductio).
Viewed this way, there’s an obvious relationship with the formal-agent problem of “I can prove what option is best, and I know I’ll take the best option—therefore, if I do something else all logical statements are conditioning on a falsehood, and so it’s true that I can get the best results by doing nothing.” The solution there is to not use logical conditioning inside the decision-making process like that, and instead use causal insertion
Similarly, we might never expect the second player in an ordered Prisoner’s Dilemma to have to deal with cooperation. But we can still talk about that counterfactual by declaring by fiat that the first move was cooperation and looking at the choices that result. Note the similarity between causal insertion and the trembling hand—almost like this trembling hand stuff works for a deeper reason. If our second PD player is an ordinary classical agent, they will choose Defect—problem resolved.
The game you present has an extra dimension, but upon learning that B or C were chosen (again, via causal surgery, not logical conditioning), a classical agent without additional information will just play the Nash equilibrium of the sub-game where only B or C are available—see JGWeissman’s comment for the correct numbers.