If we are looking for a known game structure with a formal name, I’d say it’s Battle of the Sexes: a defect-cooperate is preferable to both defect-defect and cooperate-cooperate, but each side would rather be the defector in that outcome.
Even assuming simultaneous moves, it’s not battle of the sexes. In my own classification it would be at the intersection between Too Many Cooks and Farmer’s Dilemma: Y>W>X=Z with X+Y>2W. (W=100,X=0,Y=150,Z=0.)
I didn’t mention BoS in that post because it doesn’t fit the schema. But (suddenly obviously) it fits if you just relabel one player’s moves. Then it has X>Y>W≥Z or Y>X>W=Z, making it Anti-Coordination in either case.
Why X=Z? The participants may have a preference for one nonprofit over the other, but surely—all else being equal—they should prefer their less favorite nonprofit to get money over it getting nothing.
I’d go even farther—this is charity, so instead of a social outcome which is the sum of the players’ utility the individual utilities here are applications of the players’ value functions on the social outcome. Even if you prefer one nonprofit over the other—do you prefer it enough to relinquish these extra $100? Do you think your favorite charity can do with $100 more than your second favorite can do with $200?
I don’t think so. We have X>W here—and overall Y>X>W>Z.
For most game it’s clear what counts as cooperation and what counts as defecting. For BoS—no so much. Your classification relies on that labeling (otherwise you could switch W with Z and X with Y) and since we can’t use them here I’ll just fix W>Z - that is cooperation is always the strategy that chosen by both players is better than the other strategy if chosen by both.
So—in BoS cooperation is doing what you were already wanting to do, and you hope for your spouse to defect. The order is X>Y>W>Z, which is not exactly our case but closer than any other game I can think of.
No, it’s not the same game at all because Battle of the Sexes has simultaneous moves, while this game has sequential moves (you can check the comments for other players’ moves before making your own).
The first mover can commit by just waiting 20 minutes, after which there’s a time interval equal to the period between when the first and second movers took their turns, during which the second mover can undo but the first mover can’t.
Oh. Good point. Maybe it would be interesting to do a version where you can’t retract a counter nuke after the original nuke’s 20 minutes.
Either way, I think the 20 minute rule is important for even talking about precommitting. Without it, people can chat and make contracts all they want, only for someone completely uninvolved in the conversation to suddenly post a nuke comment.
Another way to run this would be to have a period of time before launches are possible for people to negotiate, and then to not allow retracting nukes after that point. And I think next time I would make it so that the total of no-nukes would be greater than the total if only one side nuked, though I did like this time that people had the option of a creative solution that “nuked” a side but lead to higher EV for both parties than not nuking.
You also need to only permit people who took part in the negotiations to launch nukes. Otherwise newcomers could just nuke without anyone having a chance to establish a precommittment to retaliate against them.
If we are looking for a known game structure with a formal name, I’d say it’s Battle of the Sexes: a defect-cooperate is preferable to both defect-defect and cooperate-cooperate, but each side would rather be the defector in that outcome.
Even assuming simultaneous moves, it’s not battle of the sexes. In my own classification it would be at the intersection between Too Many Cooks and Farmer’s Dilemma: Y>W>X=Z with X+Y>2W. (W=100,X=0,Y=150,Z=0.)
I didn’t mention BoS in that post because it doesn’t fit the schema. But (suddenly obviously) it fits if you just relabel one player’s moves. Then it has X>Y>W≥Z or Y>X>W=Z, making it Anti-Coordination in either case.
Why X=Z? The participants may have a preference for one nonprofit over the other, but surely—all else being equal—they should prefer their less favorite nonprofit to get money over it getting nothing.
I’d go even farther—this is charity, so instead of a social outcome which is the sum of the players’ utility the individual utilities here are applications of the players’ value functions on the social outcome. Even if you prefer one nonprofit over the other—do you prefer it enough to relinquish these extra $100? Do you think your favorite charity can do with $100 more than your second favorite can do with $200?
I don’t think so. We have X>W here—and overall Y>X>W>Z.
For most game it’s clear what counts as cooperation and what counts as defecting. For BoS—no so much. Your classification relies on that labeling (otherwise you could switch W with Z and X with Y) and since we can’t use them here I’ll just fix W>Z - that is cooperation is always the strategy that chosen by both players is better than the other strategy if chosen by both.
So—in BoS cooperation is doing what you were already wanting to do, and you hope for your spouse to defect. The order is X>Y>W>Z, which is not exactly our case but closer than any other game I can think of.
No, it’s not the same game at all because Battle of the Sexes has simultaneous moves, while this game has sequential moves (you can check the comments for other players’ moves before making your own).
The ability to cancel launches make it effectively simultaneous, because they mean you can’t commit (at least not under the explicit rules)
The first mover can commit by just waiting 20 minutes, after which there’s a time interval equal to the period between when the first and second movers took their turns, during which the second mover can undo but the first mover can’t.
Oh. Good point. Maybe it would be interesting to do a version where you can’t retract a counter nuke after the original nuke’s 20 minutes.
Either way, I think the 20 minute rule is important for even talking about precommitting. Without it, people can chat and make contracts all they want, only for someone completely uninvolved in the conversation to suddenly post a nuke comment.
Another way to run this would be to have a period of time before launches are possible for people to negotiate, and then to not allow retracting nukes after that point. And I think next time I would make it so that the total of no-nukes would be greater than the total if only one side nuked, though I did like this time that people had the option of a creative solution that “nuked” a side but lead to higher EV for both parties than not nuking.
You also need to only permit people who took part in the negotiations to launch nukes. Otherwise newcomers could just nuke without anyone having a chance to establish a precommittment to retaliate against them.