English
Related papers

Related papers: Fair and Square: Cake-cutting in Two Dimensions

200 papers

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

In this article we propose a probabilistic framework in order to study the fair division of a divisible good, e.g., a cake, between n players. Our framework follows the same idea than the ''Full independence model'' used in the study of…

Computational Complexity · Computer Science 2021-08-25 Guillaume Chèze

We study searching and sorting in rounds motivated by a fair division question: given a cake cutting problem with $n$ players, compute a fair allocation in at most $k$ rounds of interaction with the players. Rounds interpolate between the…

Data Structures and Algorithms · Computer Science 2023-11-21 Simina Brânzei , Dimitris Paparas , Nicholas Recker

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

The classic cake cutting problem concerns the fair allocation of a heterogeneous resource among interested agents. In this paper, we study a public goods variant of the problem, where instead of competing with one another for the cake, the…

Computer Science and Game Theory · Computer Science 2025-01-31 Xiaohui Bei , Xinhang Lu , Warut Suksompong

We study the recently introduced cake-cutting setting in which the cake is represented by an undirected graph. This generalizes the canonical interval cake and allows for modeling the division of road networks. We show that when the graph…

Computer Science and Game Theory · Computer Science 2021-05-12 Edith Elkind , Erel Segal-Halevi , Warut Suksompong

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

We propose an online form of the cake cutting problem. This models situations where players 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 2010-07-06 Toby Walsh

In the classic cake-cutting problem (Steinhaus, 1948), a heterogeneous resource has to be divided among n agents with different valuations in a proportional way --- giving each agent a piece with a value of at least 1/n of the total. In…

Computer Science and Game Theory · Computer Science 2017-06-05 Erel Segal-Halevi , Balázs Sziklai

We study fair division of divisible goods under generalized assignment constraints. Here, each good has an agent-specific value and size, and every agent has a budget constraint that limits the total size of the goods she can receive. Since…

Computer Science and Game Theory · Computer Science 2026-03-03 Siddharth Barman , Ioannis Caragiannis , Sudarshan Shyam

Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion. These Notes provide a succinct introduction to the field. We cover three main topics. First, we…

Artificial Intelligence · Computer Science 2018-06-13 Ulle Endriss

We consider the setting of repeated fair division between two players, denoted Alice and Bob, with private valuations over a cake. In each round, a new cake arrives, which is identical to the ones in previous rounds. Alice cuts the cake at…

Computer Science and Game Theory · Computer Science 2024-02-20 Simina Brânzei , MohammadTaghi Hajiaghayi , Reed Phillips , Suho Shin , Kun Wang

We study resource allocation in two-sided markets from a fundamental perspective and introduce a general modeling and algorithmic framework to effectively incorporate the complex and multidimensional aspects of fairness. Our main technical…

Computer Science and Game Theory · Computer Science 2025-06-03 Javier Cembrano , Andrés Moraga , Victor Verdugo

We study the fair division of a continuous resource, such as a land-estate or a time-interval, among pre-specified groups of agents, such as families. Each family is given a piece of the resource and this piece is used simultaneously by all…

Computer Science and Game Theory · Computer Science 2020-10-26 Erel Segal-Halevi , Shmuel Nitzan

We consider a setting in which a single divisible good ("cake") needs to be divided between n players, each with a possibly different valuation function over pieces of the cake. For this setting, we address the problem of finding divisions…

Computer Science and Game Theory · Computer Science 2016-11-11 Yonatan Aumann , Yair Dombb , Avinatan Hassidim

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

This work develops algorithmic results for the classic cake-cutting problem in which a divisible, heterogeneous resource (modeled as a cake) needs to be partitioned among agents with distinct preferences. We focus on a standard formulation…

Computer Science and Game Theory · Computer Science 2021-05-13 Siddharth Barman , Nidhi Rathi

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 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