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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…

Computer Science and Game Theory · Computer Science 2010-10-27 Elchanan Mossel , Omer Tamuz

Given a set of $p$ players we consider problems concerning envy-free allocation of collections of $k$ pieces from a given set of goods or chores. We show that if $p\le n$ and each player can choose $k$ pieces out of $n$ pieces of a cake,…

Combinatorics · Mathematics 2017-10-27 Kathryn Nyman , Francis Edward Su , Shira Zerbib

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

In this paper, we consider the classic fair division problem of allocating $m$ divisible items to $n$ agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the…

Computer Science and Game Theory · Computer Science 2024-11-18 Yannan Bai , Kamesh Munagala , Yiheng Shen , Ian Zhang

We consider the problem of fairly dividing a two dimensional heterogeneous good among multiple players. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols primarily…

Computer Science and Game Theory · Computer Science 2019-11-27 Erel Segal-Halevi , Avinatan Hassidim , Yonatan Aumann

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

We initiate the study of multi-layered cake cutting with the goal of fairly allocating multiple divisible resources (layers of a cake) among a set of agents. The key requirement is that each agent can only utilize a single resource at each…

Computer Science and Game Theory · Computer Science 2020-04-29 Hadi Hosseini , Ayumi Igarashi , Andrew Searns

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

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

We prove several results addressing the envy-free division problem in the presence of an unpredictable (secretive) player, called the "dragon". There are two basic scenarios. 1. There are $r-1$ players and a dragon. Once the "cake" is…

Combinatorics · Mathematics 2022-02-01 Gaiane Panina , Rade Živaljević

We study the fair division problem on divisible heterogeneous resources (the cake cutting problem) with strategic agents, where each agent can manipulate his/her private valuation in order to receive a better allocation. A…

Computer Science and Game Theory · Computer Science 2023-03-31 Xiaolin Bu , Jiaxin Song , Biaoshuai Tao

Cake cutting is a classic model for studying fair division of a heterogeneous, divisible resource among agents with individual preferences. Addressing cake division under a typical requirement that each agent must receive a connected piece…

Computer Science and Game Theory · Computer Science 2023-04-28 Siddharth Barman , Pooja Kulkarni

We study the existence of fair distributions when we have more guests than pieces to allocate, focusing on envy-free distributions among those who receive a piece. The conditions on the demand from the guests can be weakened from those of…

Computer Science and Game Theory · Computer Science 2022-06-16 Pablo Soberón

In this article we study the problem of fair division. In particular we study a notion introduced by J. Barbanel that generalizes super envy-free fair division. We give a new proof of his result. Our approach allows us to give an explicit…

Computer Science and Game Theory · Computer Science 2017-07-11 Guillaume Chèze , Luca Amodei

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

A matching in a bipartite graph with parts X and Y is called envy-free if no unmatched vertex in X is a adjacent to a matched vertex in Y. Every perfect matching is envy-free, but envy-free matchings exist even when perfect matchings do…

Data Structures and Algorithms · Computer Science 2022-04-15 Elad Aigner-Horev , Erel Segal-Halevi

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

The paper considers fair allocation of resources that are already allocated in an unfair way. This setting requires a careful balance between the fairness considerations and the rights of the present owners. The paper presents re-division…

Computer Science and Game Theory · Computer Science 2022-06-01 Erel Segal-Halevi

We study fair mechanisms for the classic job scheduling problem on unrelated machines with the objective of minimizing the makespan. This problem is equivalent to minimizing the egalitarian social cost in the fair division of chores. The…

Computer Science and Game Theory · Computer Science 2024-12-12 Michal Feldman , Jugal Garg , Vishnu V. Narayan , Tomasz Ponitka

The classical approach to envy-free division and equilibrium problems relies on Knaster-Kuratowski-Mazurkiewicz theorem, Sperner's lemma or some extension involving mapping degree. We propose a different and relatively novel approach where…

Combinatorics · Mathematics 2021-03-19 Gaiane Panina , Rade Živaljević