## Olivetti Club

Kelsey Houston-EdwardsCornell University
Achieving rental harmony with a secretive roommate
Tuesday, February 13, 2018 - 4:30pm
Malott 406

In 1999, F. Su proved that, given the subjective preferences of~$n$ roommates in an~$n$-bedroom apartment, one can use Sperner's lemma to find a division of the rent such that each roommate prefers a distinct room. At the resulting rent division, no roommate has a strictly stronger preference for a different room. In this talk, I'll present Su's proof and a recent result (joint with F. Frick and F. Meunier): the subjective preferences of only~$n-1$ of the roommates actually suffice to achieve this envy-free rent division. The proof yields an algorithm to find such a division of rent.

Refreshments will be served in the lounge at 4:00 PM.