I don’t in general think there’s anything wrong with comparing utilities between people in these things—that’s what I’m doing when I talk about whether 2W>X+Y - but it would be simpler not to do so. Still, even then I think extending to all 8 would give far too many possibilities to be manually tractable—I make it 4!⋅4!/2=288.
But it wouldn’t be too hard to write a program to classify them according to Nash equilibria, if someone wanted to do that. That might be a decent start.
I don’t in general think there’s anything wrong with comparing utilities between people in these things—that’s what I’m doing when I talk about whether 2W>X+Y - but it would be simpler not to do so. Still, even then I think extending to all 8 would give far too many possibilities to be manually tractable—I make it 4!⋅4!/2=288.
But it wouldn’t be too hard to write a program to classify them according to Nash equilibria, if someone wanted to do that. That might be a decent start.