You’ve succeeded in convincing me that I’m confused about this problem, and don’t know how to make decisions in problems like this.
There’re two types of players in this game: those that win the logical lottery and those that lose (here, paperclip maximizer is a winner, and staple maximizer is a loser). A winner can either cooperate or defect against its loser opponent, with cooperation giving the winner 0 and loser 10^20, and defection giving the winner 10^10 and loser 0.
If a player doesn’t know whether it’s a loser or a winner, coordinating cooperation with its opponent has higher expected utility than coordinating defection, with mixed strategies presenting options for bargaining (the best coordinated strategy for a given player is to defect, with opponent cooperating). Thus, we have a full-fledged Prisoner’s Dilemma.
On the other hand, obtaining information about your identity (loser or winner) transforms the problem into one where you seemingly have only the choice between 0 and 10^10 (if you’re a winner), or always 0 with no ability to bargain for more (if you’re a loser). Thus, it looks like knowledge of a fact turns a problem into one of lower expected utility, irrespective of what the fact turns out to be, and takes away the incentives that would’ve made a higher win (10^20) possible. This doesn’t sound right, there should be a way of making the 10^20 accessible.
It’s like an instance of the problem involves not two, but four agents that should coordinate: a possible winner/loser pair, and a corresponding impossible pair. The impossible pair has a bizarre property that they know themselves to be impossible, like self-defeating theories PA+NOT(Con(PA)) (except that we’re talking about agent-provability and not provability), which doesn’t make them unable to reason. These four agents could form a coordinated decision, where the coordinated decision problem is obtained by throwing away the knowledge that’s not common between these four agents, in particular the digit of pi and winner/loser identity. After the decision is made, they plug back their particular information.
Edit: Nope, I changed my mind back.
You’ve succeeded in convincing me that I’m confused about this problem, and don’t know how to make decisions in problems like this.
There’re two types of players in this game: those that win the logical lottery and those that lose (here, paperclip maximizer is a winner, and staple maximizer is a loser). A winner can either cooperate or defect against its loser opponent, with cooperation giving the winner 0 and loser 10^20, and defection giving the winner 10^10 and loser 0.
If a player doesn’t know whether it’s a loser or a winner, coordinating cooperation with its opponent has higher expected utility than coordinating defection, with mixed strategies presenting options for bargaining (the best coordinated strategy for a given player is to defect, with opponent cooperating). Thus, we have a full-fledged Prisoner’s Dilemma.
On the other hand, obtaining information about your identity (loser or winner) transforms the problem into one where you seemingly have only the choice between 0 and 10^10 (if you’re a winner), or always 0 with no ability to bargain for more (if you’re a loser). Thus, it looks like knowledge of a fact turns a problem into one of lower expected utility, irrespective of what the fact turns out to be, and takes away the incentives that would’ve made a higher win (10^20) possible. This doesn’t sound right, there should be a way of making the 10^20 accessible.
It’s like an instance of the problem involves not two, but four agents that should coordinate: a possible winner/loser pair, and a corresponding impossible pair. The impossible pair has a bizarre property that they know themselves to be impossible, like self-defeating theories PA+NOT(Con(PA)) (except that we’re talking about agent-provability and not provability), which doesn’t make them unable to reason. These four agents could form a coordinated decision, where the coordinated decision problem is obtained by throwing away the knowledge that’s not common between these four agents, in particular the digit of pi and winner/loser identity. After the decision is made, they plug back their particular information.