I think this gets at one of the central problems with the concept of game-theoretic threats. I don’t know if anyone ever figured out an especially solid formal solution — it sort of comes down to finding some reasonable conception of a privileged null (or default) action, as I understand it.
I think it comes down to notions of fairness. And it can’t be within game theory, it has to be outside of it, because of scaling issues.
Imagine Alice and Bob are dividing a bunch of apples. Alice says “let’s split them evenly”. Bob says “no, my utility scale assigns 2 utility to each apple while yours assigns only 1″ (because Bob scaled his utility function, keeping his behavior the same). Or Bob says “no, my utility function assigns 2 utility to each apple because I’m hungrier” and Alice says “no, it should be less because you’re heavier” and so on. That’s why the notion of fairness can’t be derived just from the numbers of the game, it has to pull in other considerations.
Yeah, I’m not totally sure but it does seem reasonably plausible to me that it requires caring about structural details that game theory tends to factor out. One might hope you could derive the relevant concept of “fairness” from the game theory, but… I’m not particularly sure you can.
I think this gets at one of the central problems with the concept of game-theoretic threats. I don’t know if anyone ever figured out an especially solid formal solution — it sort of comes down to finding some reasonable conception of a privileged null (or default) action, as I understand it.
I think it comes down to notions of fairness. And it can’t be within game theory, it has to be outside of it, because of scaling issues.
Imagine Alice and Bob are dividing a bunch of apples. Alice says “let’s split them evenly”. Bob says “no, my utility scale assigns 2 utility to each apple while yours assigns only 1″ (because Bob scaled his utility function, keeping his behavior the same). Or Bob says “no, my utility function assigns 2 utility to each apple because I’m hungrier” and Alice says “no, it should be less because you’re heavier” and so on. That’s why the notion of fairness can’t be derived just from the numbers of the game, it has to pull in other considerations.
I tried to write more about this a couple years ago.
Yeah, I’m not totally sure but it does seem reasonably plausible to me that it requires caring about structural details that game theory tends to factor out. One might hope you could derive the relevant concept of “fairness” from the game theory, but… I’m not particularly sure you can.