Truthful fair division without free disposal

Abstract

We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

Fair cake-cutting in practice

“…There are several theoretical studies regarding the strategic properties of cake-cutting protocols [13,14], and various sophisticated protocols that are truthful under some assumptions on the valuations. See [47], [44], [42], [17], [4] and [5]. The repeated-cake-cutting setting has been studied by [20].…”

Fair cake-cutting algorithms with real land-value data

“…The gain from strategic manipulations can be entirely eliminated by using a truthful cake-cutting algorithm. Chen et al [19] and Bei et al [8] present truthful algorithms mainly for the special case of piecewise-uniform valuations, where each agent values each region of the cake at either 0 or 1. They have algorithms for more general piecewise-constant valuations, but they assume a 1-dimensional cake and do not guarantee connectivity, so they are not applicable to our setting.…”

Contiguous Cake Cutting: Hardness Results and Approximation Algorithms

“…The cake serves as a metaphor for any divisible resource such as time or land, and our aim is to perform the division in a fair manner. This problem has a long and storied history that dates back over 70 years (Steinhaus, 1948;Dubins & Spanier, 1961;Stromquist, 1980;Brams & Taylor, 1995;Su, 1999;Stromquist, 2008;Edmonds & Pruhs, 2011;Aziz & Mackenzie, 2016) and has received considerable attention from artificial intelligence researchers in the past decade (Caragiannis et al, 2011;Bei et al, 2012;Aumann et al, 2013;Balkanski et al, 2014;Brânzei & Miltersen, 2015;Alijani et al, 2017;Menon & Larson, 2017;Bei et al, 2018;Segal-Halevi, 2018;Hosseini et al, 2020).…”