How about this way of dividing the pie: Alice and Bob describe theirs needs to a third party, and the third party gives each one what is needed. Or if no third party: just describe and justify your needs in an envelope, open both simultaneously, and share the pie.
The logic that "of course, everyone should take as much as they can" is an impasse. It doesnt make anyone truly happy, makes the person with the worse fallback an inferior to the other party during the negotiations, doesnt guarantee fairness, etc. And worst of all: it doesnt allow for human values such as empathy.
This article is an algorithm between programs, not any reasonable way to treat a person, valuing their feeelings and needs.