It initially seems unintuitive that as players’ strategies improve, their collective Power tends to decrease. The proximate cause of this effect is something like “as your strategy improves, other players lose the power to capitalize off of your mistakes”.
“I disagree. The whole point of a zero-sum game (or even constant sum game) is that not everyone can win. So playing better means quite intuitively that the others can be less sure of accomplishing their own goals.”
IMO, the unintuitive and potentially problematic thing is not that in a zero-sum game playing better makes things worse for everybody else. That part is fine. The unintuitive and potentially problematic thing is that, according to this formalism, the total collective Power is greater the worse everybody plays. This seems adjacent to saying that everybody would be better off if everyone played poorly, which is true in some games (maybe) but definitely not true in zero-sum games. (Right? This isn’t my area of expertise)
EDIT: Currently I suppose what you’d say is that power =/= utility, and so even though we’d all have more power if we were all less competent, we wouldn’t actually be better off. But perhaps a better way forward would be to define a new concept of “Useful power” or something like that, which equals your share of the total power in a zero-sum game. Then we could say that everyone getting less competent wouldn’t result in everyone becoming more usefully-powerful, which seems like an important thing to be able to say. Ideally we could just redefine power that way instead of inventing a new concept of useful power, but maybe that would screw up some of your earlier theorems?
But perhaps a better way forward would be to define a new concept of “Useful power” or something like that, which equals your share of the total power in a zero-sum game.
I don’t see why useful power is particularly useful, since it’s taking a non-constant-sum quantity (outside of nash equilibria) and making it constant-sum, which seems misleading.
But I also don’t see a problem with the “better play → less exploitability → less total Power” reasoning. this feels like a situation where our naive intuitions about power are just wrong, and if you think about it more, the formal result reflects a meaningful phenomenon.
this feels like a situation where our naive intuitions about power are just wrong, and if you think about it more, the formal result reflects a meaningful phenomenon.
Different strokes for different folks, I guess. It feels very different to me.
“I disagree. The whole point of a zero-sum game (or even constant sum game) is that not everyone can win. So playing better means quite intuitively that the others can be less sure of accomplishing their own goals.”
IMO, the unintuitive and potentially problematic thing is not that in a zero-sum game playing better makes things worse for everybody else. That part is fine. The unintuitive and potentially problematic thing is that, according to this formalism, the total collective Power is greater the worse everybody plays. This seems adjacent to saying that everybody would be better off if everyone played poorly, which is true in some games (maybe) but definitely not true in zero-sum games. (Right? This isn’t my area of expertise)
EDIT: Currently I suppose what you’d say is that power =/= utility, and so even though we’d all have more power if we were all less competent, we wouldn’t actually be better off. But perhaps a better way forward would be to define a new concept of “Useful power” or something like that, which equals your share of the total power in a zero-sum game. Then we could say that everyone getting less competent wouldn’t result in everyone becoming more usefully-powerful, which seems like an important thing to be able to say. Ideally we could just redefine power that way instead of inventing a new concept of useful power, but maybe that would screw up some of your earlier theorems?
I don’t see why useful power is particularly useful, since it’s taking a non-constant-sum quantity (outside of nash equilibria) and making it constant-sum, which seems misleading.
But I also don’t see a problem with the “better play → less exploitability → less total Power” reasoning. this feels like a situation where our naive intuitions about power are just wrong, and if you think about it more, the formal result reflects a meaningful phenomenon.
Different strokes for different folks, I guess. It feels very different to me.