For those who aren’t familiar with it, here’s a description of the game. Each player receives a complete suit of standard playing cards, ranked Ace low through King high. Another complete suit, the diamonds, is shuffled (or not, if you want a game of complete information) and put face down on the table; these diamonds have point values Ace=1 through King=13. In each trick, one diamond is flipped face-up. Each player then chooses one card from their own hand to bid for the face-up diamonds, and all bids are revealed simultaneously. Whoever bids highest wins the face-up diamonds, but if there is a tie for the highest bid (even when other players did not tie), then no one wins them and they remain on the table to be won along with the next trick. All bids are discarded after every trick.
Especially when the King comes up early, you can see everyone looking at each other trying to figure out how many levels deep to evaluate “What will the other players do?”.
(1) Play my King to be likely to win.
(2) Everyone else is likely to do (1) also, which will waste their Kings. So instead play low while they throw away their Kings.
(3) If the players are paying attention, they might all realize they should (2), in which case I should play highest low card—the Queen.
(4+) The 4th+ levels could repeat (2) and (3) mutatis mutandis until every card has been the optimal choice at some level. In practice, players immediately recognize the futility of that line of thought and instead shift to the question: How far down the chain of reasoning are the other players likely to go? And that tends to depend on knowing the people involved and the social context of the game.
Maybe playing GOPS should be added to the repertoire of difficult decision theory puzzles alongside the prisoner’s dilemma, Newcomb’s problem, Pascal’s mugging, and the rest of that whole intriguing panoply. We’ve had a Prisoner’s Dilemma competition here before—would anyone like to host a GOPS competition?
I’m going to play this game at LW meetups in future. Hopefully some insights will arise out of it.
I also think I might try to generalise this kind of problem, in the vein of trolley problems being a generalisation of some types of decisions and Parfit’s Hitchhiker being a generalisation of precommittment-favouring situations.
Problem 2 reminds me strongly of playing GOPS.
For those who aren’t familiar with it, here’s a description of the game. Each player receives a complete suit of standard playing cards, ranked Ace low through King high. Another complete suit, the diamonds, is shuffled (or not, if you want a game of complete information) and put face down on the table; these diamonds have point values Ace=1 through King=13. In each trick, one diamond is flipped face-up. Each player then chooses one card from their own hand to bid for the face-up diamonds, and all bids are revealed simultaneously. Whoever bids highest wins the face-up diamonds, but if there is a tie for the highest bid (even when other players did not tie), then no one wins them and they remain on the table to be won along with the next trick. All bids are discarded after every trick.
Especially when the King comes up early, you can see everyone looking at each other trying to figure out how many levels deep to evaluate “What will the other players do?”.
(1) Play my King to be likely to win. (2) Everyone else is likely to do (1) also, which will waste their Kings. So instead play low while they throw away their Kings. (3) If the players are paying attention, they might all realize they should (2), in which case I should play highest low card—the Queen. (4+) The 4th+ levels could repeat (2) and (3) mutatis mutandis until every card has been the optimal choice at some level. In practice, players immediately recognize the futility of that line of thought and instead shift to the question: How far down the chain of reasoning are the other players likely to go? And that tends to depend on knowing the people involved and the social context of the game.
Maybe playing GOPS should be added to the repertoire of difficult decision theory puzzles alongside the prisoner’s dilemma, Newcomb’s problem, Pascal’s mugging, and the rest of that whole intriguing panoply. We’ve had a Prisoner’s Dilemma competition here before—would anyone like to host a GOPS competition?
I’m going to play this game at LW meetups in future. Hopefully some insights will arise out of it.
I also think I might try to generalise this kind of problem, in the vein of trolley problems being a generalisation of some types of decisions and Parfit’s Hitchhiker being a generalisation of precommittment-favouring situations.