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Related papers: A Discrete and Bounded Envy-free Cake Cutting Prot…

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In this article we study a cake cutting problem. More precisely, we study symmetric fair division algorithms, that is to say we study algorithms where the order of the players do not influence the value obtained by each player. In the first…

Computer Science and Game Theory · Computer Science 2019-10-14 Guillaume Chèze

We consider the fair division problem of indivisible items. It is well-known that an envy-free allocation may not exist, and a relaxed version of envy-freeness, envy-freeness up to one item (EF1), has been widely considered. In an EF1…

Computer Science and Game Theory · Computer Science 2022-11-30 Xiaolin Bu , Zihao Li , Shengxin Liu , Jiaxin Song , Biaoshuai Tao

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

Given a set of n sticks of various (not necessarily different) lengths, what is the largest length so that we can cut k equally long pieces of this length from the given set of sticks? We analyze the structure of this problem and show that…

Data Structures and Algorithms · Computer Science 2017-11-06 Raphael Reitzig , Sebastian Wild

We consider the problem of fairly dividing a set of heterogeneous divisible resources among agents with different preferences. We focus on the setting where the resources correspond to the edges of a connected graph, every agent must be…

Data Structures and Algorithms · Computer Science 2023-12-13 Argyrios Deligkas , Eduard Eiben , Robert Ganian , Thekla Hamm , Sebastian Ordyniak

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,…

Computer Science and Game Theory · Computer Science 2020-09-15 Xiaohui Bei , Guangda Huzhang , Warut Suksompong

We study the paradigmatic fair division problem of allocating a divisible good among agents with heterogeneous preferences, commonly known as cake cutting. Classical cake cutting protocols are susceptible to manipulation. Do their strategic…

Computer Science and Game Theory · Computer Science 2016-07-20 Simina Brânzei , Ioannis Caragiannis , David Kurokawa , Ariel D. Procaccia

Fair division has emerged as a very hot topic in multiagent systems, and envy-freeness is among the most compelling fairness concepts. An allocation of indivisible items to agents is envy-free if no agent prefers the bundle of any other…

Computer Science and Game Theory · Computer Science 2021-02-26 Ioannis Caragiannis , Stavros Ioannidis

The undercut procedure was presented by Brams et al. [2] as a procedure for identifying an envy-free allocation when agents have preferences over sets of objects. They assumed that agents have strict preferences over objects and their…

Computer Science and Game Theory · Computer Science 2014-02-11 Haris Aziz

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 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

We study the existence of allocations of indivisible goods that are envy-free up to one good (EF1), under the additional constraint that each bundle needs to be connected in an underlying item graph. If the graph is a path and the utility…

Computer Science and Game Theory · Computer Science 2022-05-23 Vittorio Bilò , Ioannis Caragiannis , Michele Flammini , Ayumi Igarashi , Gianpiero Monaco , Dominik Peters , Cosimo Vinci , William S. Zwicker

We study the problem of fairly allocating indivisible items and a desirable heterogeneous divisible good (i.e., cake) to agents with additive utilities. In our paper, each indivisible item can be a good that yields non-negative utilities to…

Computer Science and Game Theory · Computer Science 2025-11-10 Haris Aziz , Xinhang Lu , Simon Mackenzie , Mashbat Suzuki

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

Finding an envy-free allocation of indivisible resources to agents is a central task in many multiagent systems. Often, non-trivial envy-free allocations do not exist, and, when they do, finding them can be computationally hard. Classical…

Computer Science and Game Theory · Computer Science 2020-11-24 Robert Bredereck , Andrzej Kaczmarczyk , Rolf Niedermeier

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

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

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

We study the problem of Envy-Free Incomplete Connected Fair Division, where exactly p vertices of an undirected graph must be allocated to agents such that each agent receives a connected share and does not envy another agent's share.…

Data Structures and Algorithms · Computer Science 2025-12-30 Ajaykrishnan E S , Daniel Lokshtanov

We consider the classic cake-cutting problem of producing fair allocations for $n$ agents, in the Robertson-Webb query model. In this model, it is known that: (i) proportional allocations can be computed using $O(n \log n)$ queries, and…

Computer Science and Game Theory · Computer Science 2025-06-17 Arnav Mehra , Alexandros Psomas