Two-Person Cake-Cutting: The Optimal Number of Cuts

Optimal Envy-Free Cake Cutting

We consider the problem of fairly dividing a heterogeneous divisible good among agents with different preferences. Previous work has shown that envy-free allocations, i.e., where each agent prefers its own allocation to any other, may not be efficient, in the sense of maximizing the total value of the agents. Our goal is to pinpoint the most efficient allocations among all envy-free allocations...

Cake-Cutting with Different Entitlements: How Many Cuts are Needed?

A cake has to be divided fairly among n agents. When all agents have equal entitlements, it is known that such a division can be implemented with n − 1 cuts. When agents may have different entitlements, we show that at least 2n − 2 cuts may be necessary, and 2n · Θ(log(n)) cuts are always sufficient.

Optimal Proportional Cake Cutting with Connected Pieces

We consider the classic cake cutting problem where one allocates a divisible cake to n participating agents. Among all valid divisions, fairness and efficiency (a.k.a. social welfare) are the most critical criteria to satisfy and optimize, respectively. We study computational complexity of computing an efficiency optimal division given the conditions that the allocation satisfies proportional f...

Two-Person Pie-Cutting

N-Person Cake-Cutting: There May Be No Perfect Division

A cake is a metaphor for a heterogeneous, divisible good, such as land. A perfect division of cake is efficient (also called Pareto-optimal), envyfree, and equitable. We give an example of a cake in which it is impossible to divide it among three players such that these three properties are satisfied, however many cuts are made. It turns out that two of the three properties can be satisfied by ...