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

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This paper is part of an ongoing endeavor to bring the theory of fair division closer to practice by handling requirements from real-life applications. We focus on two requirements originating from the division of land estates: (1) each…

Computer Science and Game Theory · Computer Science 2023-03-24 Edith Elkind , Erel Segal-Halevi , Warut Suksompong

Cake-cutting is a playful name for the fair division of a heterogeneous, divisible good among agents, a well-studied problem at the intersection of mathematics, economics, and artificial intelligence. The cake-cutting literature is rich and…

Computer Science and Game Theory · Computer Science 2023-11-23 Peter Kern , Daniel Neugebauer , Jörg Rothe , René L. Schilling , Dietrich Stoyan , Robin Weishaupt

Cake-cutting protocols aim at dividing a ``cake'' (i.e., a divisible resource) and assigning the resulting portions to several players in a way that each of the players feels to have received a ``fair'' amount of the cake. An important…

Computer Science and Game Theory · Computer Science 2009-10-19 Claudia Lindner , Joerg Rothe

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

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

Graph cut problems are fundamental in Combinatorial Optimization, and are a central object of study in both theory and practice. Furthermore, the study of \emph{fairness} in Algorithmic Design and Machine Learning has recently received…

Data Structures and Algorithms · Computer Science 2022-02-17 Michael Dinitz , Aravind Srinivasan , Leonidas Tsepenekas , Anil Vullikanti

The design of algorithms for political redistricting generally takes one of two approaches: optimize an objective such as compactness or, drawing on fair division, construct a protocol whose outcomes guarantee partisan fairness. We aim to…

Computer Science and Game Theory · Computer Science 2023-05-23 Gerdus Benadè , Ariel D. Procaccia , Jamie Tucker-Foltz

Fair division with unequal shares is an intensively studied recourse allocation problem. For $ i\in [n] $, let $ \mu_i $ be an atomless probability measure on the measurable space $(C,\mathcal{S}) $ and let $ t_i $ be positive numbers…

Combinatorics · Mathematics 2022-02-15 Zsuzsanna Jankó , Attila Joó

Cutting a cake is a metaphor for the problem of dividing a resource (cake) among several agents. The problem becomes non-trivial when the agents have different valuations for different parts of the cake (i.e. one agent may like chocolate…

Information Theory · Computer Science 2016-01-26 Payam Delgosha , Amin Gohari

We characterize methods of dividing a cake between two bidders in a way that is incentive-compatible and Pareto-efficient. In our cake cutting model, each bidder desires a subset of the cake (with a uniform value over this subset), and is…

Computer Science and Game Theory · Computer Science 2012-10-02 Avishay Maya , Noam Nisan

We study the disproportionate version of the classical cake-cutting problem: how efficiently can we divide a cake, here $[0,1]$, among $n$ agents with different demands $\alpha_1, \alpha_2, \dots, \alpha_n$ summing to $1$? When all the…

Combinatorics · Mathematics 2019-09-17 Logan Crew , Bhargav Narayanan , Sophie Spirkl

The fair division of indivisible goods is not only a subject of theoretical research, but also an important problem in practice, with solutions being offered on several online platforms. Little is known, however, about the characteristics…

Computer Science and Game Theory · Computer Science 2025-05-07 Paula Böhm , Robert Bredereck , Paul Gölz , Andrzej Kaczmarczyk , Stanisław Szufa

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

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

We study classic cake-cutting problems, but in discrete models rather than using infinite-precision real values, specifically, focusing on their communication complexity. Using general discrete simulations of classical infinite-precision…

Computer Science and Game Theory · Computer Science 2018-08-21 Simina Brânzei , Noam Nisan

We investigate the problem of fairly dividing a divisible heterogeneous resource, also known as a cake, among a set of agents who may have different entitlements. We characterize the existence of a connected strongly-proportional allocation…

Combinatorics · Mathematics 2024-08-07 Zsuzsanna Jankó , Attila Joó , Erel Segal-Halevi , Sheung Man Yuen

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

In the classical cake cutting problem, a resource must be divided among agents with different utilities so that each agent believes they have received a fair share of the resource relative to the other agents. We introduce a variant of the…

Data Structures and Algorithms · Computer Science 2018-02-27 Rediet Abebe , Jon Kleinberg , David Parkes

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

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