Truthful Fair Division

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.Comment: 10 page

Truth, justice, and cake cutting

“…The following lemma provides us with a tractable method of finding a perfect partition when the agents have piecewise linear valuation functions. 8 Mossel and Tamuz (2010) make the same observation.…”

Cake Cutting Algorithms

“…A simple randomized strategyproof, envy-free algorithm was independently discovered by Chen et al (2013) and Mossel and Tamuz (2010). Chen et al (2013) also design a more intricate deterministic strategyproof envy-free algorithm for piecewise uniform valuation functions, which is generalized by Aziz and Ye (2014); under the same assumption, Maya and Nisan (2012) give a characterization of strategyproof, Pareto-efficient cake cutting algorithms.…”

Mechanism design for fair division

“…Most results related to truthfulness were weakened by the assumption that each agent would be truthful in reporting her valuations unless this strategy was dominated. Very recent work [7,26,37,25] studies truthful cake cutting variations using the standard notion of truthfulness according to which an agent need not be truthful unless doing so is a dominant strategy. Chen et al [7] study truthful cake-cutting with agents having piecewise uniform valuations and they provide a polynomial-time mechanism that is truthful, proportional, and envy-free.…”

“…Chen et al [7] study truthful cake-cutting with agents having piecewise uniform valuations and they provide a polynomial-time mechanism that is truthful, proportional, and envy-free. They also design randomized mechanisms for more general families of valuation functions, while Mossel and Tamuz [26] prove the existence of truthful (in expectation) mechanisms satisfying proportionality in expectation for general valuations. Zivan et al [37] aim to achieve envy-free Pareto optimal allocations of multiple divisible goods while reducing, but not eliminating, the agents' incentives to lie.…”