English
Related papers

Related papers: Cake cutting: Explicit examples for impossibility …

200 papers

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

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

Machine Learning · Computer Science 2021-11-30 Mohammad Ghodsi , Amirmahdi Mirfakhar

A perfectly divisible cake is to be divided among a group of agents. Each agent is entitled to a share between zero and one, and these entitlements are compatible in that they sum to one. The mediator does not know the preferences of the…

Theoretical Economics · Economics 2025-08-13 Florian Brandl , Andrew Mackenzie

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 study the classic problem of fairly dividing a heterogeneous and divisible resource -- represented by a cake, $[0,1]$ -- among $n$ agents. This work considers an interesting variant of the problem where agents are embedded on a graph.…

Computer Science and Game Theory · Computer Science 2022-11-16 Ganesh Ghalme , Xin Huang , Nidhi Rathi

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 the envy-free cake-cutting problem we are given a resource, usually called a cake and represented as the $[0,1]$ interval, and a set of $n$ agents with heterogeneous preferences over pieces of the cake. The goal is to divide the cake…

Computer Science and Game Theory · Computer Science 2025-09-01 Alexandros Hollender , Aviad Rubinstein

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 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

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

The classical cake cutting problem studies how to find fair allocations of a heterogeneous and divisible resource among multiple agents. Two of the most commonly studied fairness concepts in cake cutting are proportionality and…

Data Structures and Algorithms · Computer Science 2019-07-15 Xiaohui Bei , Xiaoming Sun , Hao Wu , Jialin Zhang , Zhijie Zhang , Wei Zi

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

Single minded agents have strict preferences, in which a bundle is acceptable only if it meets a certain demand. Such preferences arise naturally in scenarios such as allocating computational resources among users, where the goal is to…

Computer Science and Game Theory · Computer Science 2016-04-29 Simina Brânzei , Yuezhou Lv , Ruta Mehta

We study the cake-cutting problem when agents have single-peaked preferences over the cake. We show that a recently proposed mechanism by Wang-Wu (2019) to obtain envy-free allocations can yield large welfare losses. Using a simplifying…

Computer Science and Game Theory · Computer Science 2020-03-05 Bhavook Bhardwaj , Rajnish Kumar , Josue Ortega

We study the monotonicity properties of solutions in the classic problem of fair cake-cutting --- dividing a heterogeneous resource among agents with different preferences. Resource- and population-monotonicity relate to scenarios where the…

Computer Science and Game Theory · Computer Science 2018-09-26 Erel Segal-Halevi , Balázs Sziklai

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

In contrast to common belief, the Calculus of Communicating Systems (CCS) and similar process algebras lack the expressive power to accurately capture mutual exclusion protocols without enriching the language with fairness assumptions.…

Logic in Computer Science · Computer Science 2017-09-05 Victor Dyseryn , Rob van Glabbeek , Peter Höfner

A fundamental result in cake cutting states that for any number of players with arbitrary preferences over a cake, there exists a division of the cake such that every player receives a single contiguous piece and no player is left envious.…

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

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