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

TL;DR

This paper investigates the complexity of fairly dividing a cake among agents with unequal entitlements, establishing lower and upper bounds on the number of cuts needed for such divisions.

Contribution

It introduces bounds on the number of cuts required for fair division with different entitlements, extending previous results for equal entitlements.

Findings

At least 2n - 2 cuts may be necessary for unequal entitlements.

O(n log n) cuts are sufficient for fair division with different entitlements.

The paper generalizes fair division complexity beyond equal entitlement scenarios.

Abstract

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, the paper shows that at least $2 n -2$ cuts may be necessary, and $O(n \log(n))$ cuts are always sufficient.