The algorithm is likely to ask anyone to choose a favoured room from an equal split, so in theory the algorithm won't work if someone has a smaller-than-equalit

The algorithm is likely to ask anyone to choose a favoured room from an equal split, so in theory the algorithm won't work if someone has a smaller-than-equality budget. The algorithm depends on everyone having a personal way of splitting the cost of the house so that they would be equally happy with any room. If you are only willing to spend less-than-equality on a particular room, you should be prepared to spend more-than-equality on another room to compensate. Someone without that possibility might get a result incompatible with their needs or might be taken advantage of by a knowledgeable enemy player, I would think. So in theory, no, this method won't work perfectly. But in practice, yes, you might still get a decent result. This algorithm is good for cake-cutting, since everyone likes to receive cake, but less good for rent-splitting, since not everyone likes to pay rent.