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”.
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”.