Individual pieces set

In the theory of fair cake-cutting, the individual-pieces set (IPS) is a geometric object that represents all possible utility vectors in cake partitions.

The table below describes the parts and their values.

The IPS is the set of utility vectors of all possible partitions.

With two agents, this frontier can be constructed in the following way: The IPS was introduced as part of the Dubins–Spanier theorems and used in the proof of Weller's theorem.

The term "Individual Pieces set" was coined by Julius Barbanel.