No, you are right. For certain setups (say when the set of outcomes is a perfect circle/sphere), then if one player gets everything they want, this only happens if the weight of the other player’s utility is zero.
I didn’t write up that case, because there I would have to let the thetas be zero and infinity, a subtlety that would distract from the main point.
No, you are right. For certain setups (say when the set of outcomes is a perfect circle/sphere), then if one player gets everything they want, this only happens if the weight of the other player’s utility is zero.
I didn’t write up that case, because there I would have to let the thetas be zero and infinity, a subtlety that would distract from the main point.