Mind the gap: Cake cutting with separation

Cake Cutting ∗

In the 2nd world war, if you’re a collection of Polish mathematicians sitting out the war in Lvov, your thoughts naturally turn to ... cake. Or more precisely, how to cut a cake. This is the beginning of what we now call the problem of “fair division”. Fair division algorithms are examples of what we might now call a mechanism, much like an auction. These are protocols designed to allocate reso...

13 Cake Cutting Algorithms

Imagine a cake that must be divided between a group of gluttonous children. To complicate matters, the cake is heterogeneous: two pieces of cake may differ in terms of their toppings, so the children have different preferences over the pieces (one may weakly prefer a larger proportion of chocolate curls, while another may single-mindedly desire the piece with the cherry). In this chapter we dis...

Cake Cutting Algorithms

Online Cake Cutting

We propose an online form of the cake cutting problem. This models situations where players arrive and depart during the process of dividing a resource. We show that well known fair division procedures like cut-and-choose and the Dubins-Spanier moving knife procedure can be adapted to apply to such online problems. We propose some desirable properties that online cake cutting procedures might p...

Simultaneous Cake Cutting

We introduce the simultaneous model for cake cutting (the fair allocation of a divisible good), in which agents simultaneously send messages containing a sketch of their preferences over the cake. We show that this model enables the computation of divisions that satisfy proportionality — a popular fairness notion — using a protocol that circumvents a standard lower bound via parallel informatio...