I don’t think these add very much, and I further think, if you’re proposing more than one predictor, you have to acknowledge that they’re going to model each other, and give SOME reason for them not to be perfectly symmetrical. If they’re symmetrical and know it, then (presuming they very slightly prefer spending less over spending more, if they can’t actually influence the outcome) all boxes have $1, for any player action.
Assuming stupid or semi-predictive omegas, precommitting to pick the second-fullest box seems to be the right strategy for 4-boxes (incentive for predictors to put money in everyone else’s boxes). Only a slight modification of the naive strategy for 5-boxes: break ties by picking the highest-numbered box (provide Schelling point for the predictors to all bet on, and fund, the same box).
Only for stupid/partial predictors. If they predict each other and know they’re symmetrical, nothing the agent does matters. If they’re trying to optimize against other predictors who they don’t think are as smart as they, they can hope that some will make mistakes, and they will do their best not to be biggest by putting money in all their opponents’ boxes. This is the same incentive as “pick the smallest amount” would be, but in the case that any mistakes DO get made, and there are varying amounts, the agent prefers more money to less.
Couldn’t you equally argue that they will do their best not to be smallest by not putting any money in all their opponent’s boxes? After all, “second-fullest” is the same as “third-emptiest”.
I don’t think these add very much, and I further think, if you’re proposing more than one predictor, you have to acknowledge that they’re going to model each other, and give SOME reason for them not to be perfectly symmetrical. If they’re symmetrical and know it, then (presuming they very slightly prefer spending less over spending more, if they can’t actually influence the outcome) all boxes have $1, for any player action.
Assuming stupid or semi-predictive omegas, precommitting to pick the second-fullest box seems to be the right strategy for 4-boxes (incentive for predictors to put money in everyone else’s boxes). Only a slight modification of the naive strategy for 5-boxes: break ties by picking the highest-numbered box (provide Schelling point for the predictors to all bet on, and fund, the same box).
Why would precommitting to pick the second-fullest box give an incentive for predictors to put money in everyone else’s boxes?
Only for stupid/partial predictors. If they predict each other and know they’re symmetrical, nothing the agent does matters. If they’re trying to optimize against other predictors who they don’t think are as smart as they, they can hope that some will make mistakes, and they will do their best not to be biggest by putting money in all their opponents’ boxes. This is the same incentive as “pick the smallest amount” would be, but in the case that any mistakes DO get made, and there are varying amounts, the agent prefers more money to less.
Couldn’t you equally argue that they will do their best not to be smallest by not putting any money in all their opponent’s boxes? After all, “second-fullest” is the same as “third-emptiest”.