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.
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.