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Cake-cutting is a fundamental model of dividing a heterogeneous resource, such as land, broadcast time, and advertisement space. In this study, we consider the problem of dividing a discrete cake fairly in which the indivisible goods are…

Computer Science and Game Theory · Computer Science 2022-11-29 Ayumi Igarashi

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

In contrast to the classical cake-cutting problem (how to fairly divide a desirable object), "chore division" is the problem of how to divide an undesirable object. We develop the first explicit algorithm for envy-free chore division among…

Combinatorics · Mathematics 2009-09-03 Elisha Peterson , Francis Edward Su

We study the envy-free cake-cutting problem for $d+1$ players with $d$ cuts, for both the oracle function model and the polynomial time function model. For the former, we derive a $\theta(({1\over\epsilon})^{d-1})$ time matching bound for…

Computer Science and Game Theory · Computer Science 2009-07-10 Xiaotie Deng , Qi Qi , Amin Saberi

We study the problem of fairly allocating a divisible resource in the form of a graph, also known as graphical cake cutting. Unlike for the canonical interval cake, a connected envy-free allocation is not guaranteed to exist for a graphical…

Computer Science and Game Theory · Computer Science 2024-06-18 Sheung Man Yuen , Warut Suksompong

In this note we study a problem of fair division in the absence of full information. We give an algorithm which solves the following problem: n $\ge$ 2 persons want to cut a cake into n shares so that each person will get at least 1/n of…

Multiagent Systems · Computer Science 2018-10-17 Guillaume Chèze

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

We introduce a graphical framework for fair division in cake cutting, where comparisons between agents are limited by an underlying network structure. We generalize the classical fairness notions of envy-freeness and proportionality to this…

Data Structures and Algorithms · Computer Science 2017-07-10 Xiaohui Bei , Youming Qiao , Shengyu Zhang

Consider $n$ players having preferences over the connected pieces of a cake, identified with the interval $[0,1]$. A classical theorem, found independently by Stromquist and by Woodall in 1980, ensures that, under mild conditions, it is…

Combinatorics · Mathematics 2019-01-16 Frédéric Meunier , Shira Zerbib

This article deals with the cake cutting problem. In this setting, there exists two notions of fair division: proportional division (when there are n players, each player thinks to get at least 1/n of the cake) and envy-free division (each…

Multiagent Systems · Computer Science 2025-09-17 Guillaume Chèze

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…

Combinatorics · Mathematics 2019-08-12 Erel Segal-Halevi

Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and…

Computer Science and Game Theory · Computer Science 2013-10-29 Haris Aziz , Chun Ye

Classic cake-cutting algorithms enable people with different preferences to divide among them a heterogeneous resource (``cake''), such that the resulting division is fair according to each agent's individual preferences. However, these…

Computer Science and Game Theory · Computer Science 2021-08-06 Erel Segal-Halevi , Shmuel Nitzan , Avinatan Hassidim , Yonatan Aumann

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

The fair division literature in economics considers how to divide resources between multiple agents such that the allocation is envy-free: each agent receives their favorite piece. Researchers have developed a variety of fair division…

Programming Languages · Computer Science 2023-04-11 Noah Bertram , Alex Levinson , Justin Hsu

The problem of fair division known as "cake cutting" has been the focus of multiple papers spanning several decades. The most prominent problem in this line of work has been to bound the query complexity of computing an envy-free outcome in…

Computer Science and Game Theory · Computer Science 2022-01-14 Ioannis Caragiannis , Vasilis Gkatzelis , Alexandros Psomas , Daniel Schoepflin

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

In the classic problem of fair cake-cutting, a single interval ("cake") has to be divided among n agents with different value measures, giving each agent a single sub-interval with a value of at least 1/n of the total. This paper studies a…

Combinatorics · Mathematics 2020-06-19 Erel Segal-Halevi

Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to…

Theoretical Economics · Economics 2023-03-20 Erel Segal-Halevi , Warut Suksompong

We analyze lower bounds for the number of envy-free divisions, in the classical Woodall-Stormquist setting and in a non-classical case, when envy-freeness is combined with the equipartition of a measure. 1. In the first scenario, there are…

Combinatorics · Mathematics 2025-05-08 Duško Jojić , Gaiane Panina , Rade Živaljević