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Related papers: The Query Complexity of Cake Cutting

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We consider the classic cake cutting problem in the Robertson-Webb model, with the objective of proportional fairness. We show that any randomized algorithm must use $\Omega(n \log n)$ queries.

Data Structures and Algorithms · Computer Science 2026-05-22 Stephen Arndt , Kirk Pruhs , Trung Tran

We consider the classic problem of envy-free division of a heterogeneous good ("cake") among several agents. It is known that, when the allotted pieces must be connected, the problem cannot be solved by a finite algorithm for 3 or more…

Data Structures and Algorithms · Computer Science 2018-05-15 Erel Segal-Halevi , Avinatan Hassidim , Yonatan Aumann

We consider multi-layered cake cutting in order to fairly allocate numerous divisible resources (layers of cake) among a group of agents under two constraints: contiguity and feasibility. We first introduce a new computational model in a…

Artificial Intelligence · Computer Science 2024-03-19 Mohammad Azharuddin Sanpui

We study the classic problem of \emph{fairly} dividing a heterogeneous and divisible resource -- modeled as a line segment $[0,1]$ and typically called as a \emph{cake} -- among $n$ agents. This work considers an interesting variant of the…

Computer Science and Game Theory · Computer Science 2022-11-15 Ganesh Ghalme , Xin Huang , Yuka Machino , Nidhi Rathi

We consider the well-studied cake cutting problem in which the goal is to identify a fair allocation based on a minimal number of queries from the agents. The problem has attracted considerable attention within various branches of computer…

Data Structures and Algorithms · Computer Science 2016-04-07 Haris Aziz , Simon Mackenzie

In the classical cake cutting problem, a resource must be divided among agents with different utilities so that each agent believes they have received a fair share of the resource relative to the other agents. We introduce a variant of the…

Data Structures and Algorithms · Computer Science 2018-02-27 Rediet Abebe , Jon Kleinberg , David Parkes

The classic cake-cutting problem provides a model for addressing fair and efficient allocation of a divisible, heterogeneous resource (metaphorically, the cake) among agents with distinct preferences. Focusing on a standard formulation of…

Computer Science and Game Theory · Computer Science 2021-05-21 Eshwar Ram Arunachaleswaran , Siddharth Barman , Rachitesh Kumar , Nidhi Rathi

We propose an online form of the cake cutting problem. This models situations where agents arrive and depart during the process of dividing a resource. We show that well known fair division procedures like cut-and-choose and the…

Artificial Intelligence · Computer Science 2012-04-18 Toby Walsh

A division of a cake by n people is envy free if everyone thinks they got the biggest pieces. Note that peoples tastes can differ. There is a discrete protocol for envy free division for n=3 which takes at most 5 cuts. For n=4 and beyond…

Logic · Mathematics 2015-08-25 William Gasarch

Envy-free cake-cutting protocols procedurally divide an infinitely divisible good among a set of agents so that no agent prefers another's allocation to their own. These protocols are highly complex and difficult to prove correct. Recently,…

Computer Science and Game Theory · Computer Science 2024-05-31 Noah Bertram , Tean Lai , Justin Hsu

In this article we suggest a model of computation for the cake cutting problem. In this model the mediator can ask the same queries as in the Robertson-Webb model but he or she can only perform algebraic operations as in the Blum-Shub-Smale…

Computer Science and Game Theory · Computer Science 2019-07-11 Guillaume Chèze

We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for…

Computer Science and Game Theory · Computer Science 2022-09-20 Edith Elkind , Erel Segal-Halevi , Warut Suksompong

We consider a classical envy-free cake cutting problem. The first limited protocol was proposed by Aziz and McKenzie in 2016 arXiv:1604.03655. The disadvantage of this protocol is its high complexity. The authors proved that the maximum…

Computational Complexity · Computer Science 2023-06-07 Georgy Sokolov

We examine the history of cake cutting mechanisms and discuss the efficiency of their allocations. In the case of piecewise uniform preferences, we define a game that in the presence of strategic agents has equilibria that are not dominated…

Computer Science and Game Theory · Computer Science 2012-04-10 Egor Ianovski

We introduce a generalized cake-cutting problem in which we seek to divide multiple cakes so that two players may get their most-preferred piece selections: a choice of one piece from each cake, allowing for the possibility of linked…

Combinatorics · Mathematics 2009-09-03 John Cloutier , Kathryn L. Nyman , Francis Edward Su

An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among $n$ players who value pieces according to…

Discrete Mathematics · Computer Science 2018-05-02 Ágnes Cseh , Tamás Fleiner

We study the proportional chore division problem where a protocol wants to divide an undesirable object, called chore, among $n$ different players. The goal is to find an allocation such that the cost of the chore assigned to each player be…

Computer Science and Game Theory · Computer Science 2018-05-09 Alireza Farhadi , MohammadTaghi Hajiaghayi

We consider the classical cake-cutting problem where we wish to fairly divide a heterogeneous resource, often modeled as a cake, among interested agents. Work on the subject typically assumes that the cake is represented by an interval. In…

Computer Science and Game Theory · Computer Science 2025-05-02 Xiaohui Bei , Warut Suksompong

Relying on configuration spaces and equivariant topology, we study a general "cooperative envy-free division problem". A group of players want to cut a "cake" $I=[0,1]$ and divide among themselves the pieces in an envy-free manner. Once the…

Combinatorics · Mathematics 2023-02-08 Duško Jojić , Gaiane Panina , Rade Živaljević

Using a lab experiment, we investigate the real-life performance of envy-free and proportional cake-cutting procedures with respect to fairness and preference manipulation. We find that envy-free procedures, in particular Selfridge-Conway,…

Computer Science and Game Theory · Computer Science 2022-06-01 Maria Kyropoulou , Josué Ortega , Erel Segal-Halevi