Envy Free Divisions
Seth Unruh
Abstract:
We consider the division of a single homogeneous object and transfers of
money among several people who may have different valuations for the object.
A division is envy free if every person believes the portion he or she
received is at least as valuable as the portion received by each other
person. If no money is transferred, the only envy-free division involves
each person receiving the same fraction of the object. When money transfers
are allowed, we show that the set of envy-free divisions is a simplex whose
vertices involve giving the same fraction of the object to each person in a
set of persons who most value the object, and in turn those people pay the
same amount of money to the other people who receive none of the object.