Truthful Fair Division

TL;DR

This paper develops truthful mechanisms for fair division, including cake cutting and indivisible goods, ensuring fair and risk-minimized allocations under various conditions.

Contribution

It introduces new truthful mechanisms for fair division that guarantee proportional shares and improve fairness in both divisible and indivisible settings.

Findings

Existence of truthful mechanisms guaranteeing each player at least 1/k of the cake.

Mechanisms ensuring each player gets more than 1/k when multiple measures exist.

Approximate fairness guarantees for indivisible goods as the number of goods increases.

Abstract

We address the problem of fair division, or cake cutting, with the goal of finding truthful mechanisms. In the case of a general measure space ("cake") and non-atomic, additive individual preference measures - or utilities - we show that there exists a truthful "mechanism" which ensures that each of the k players gets at least 1/k of the cake. This mechanism also minimizes risk for truthful players. Furthermore, in the case where there exist at least two different measures we present a different truthful mechanism which ensures that each of the players gets more than 1/k of the cake. We then turn our attention to partitions of indivisible goods with bounded utilities and a large number of goods. Here we provide similar mechanisms, but with slightly weaker guarantees. These guarantees converge to those obtained in the non-atomic case as the number of goods goes to infinity.