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# Envy-Free Divisions

## 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 division he or she received is at least as valuable as the division 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.

## Author Bio

I have recently graduated with a degree in Mathematics from Goshen College. I applied for the Maples Scholars program through Goshen College in the spring of 2009. The Maple Scholars program at Goshen College was my first experience in mathematical research. I enjoyed working with Dr. David Housman throughout my research and I really appreciated all his help with my result and writing my paper. Starting August 8, 2009, I will be doing a year-long stint of voluntary service in Indonesia.

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