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Related papers: How to Cut a Cake Fairly: A Generalization to Grou…

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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

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

Computer Science and Game Theory · Computer Science 2021-05-21 Eshwar Ram Arunachaleswaran , Siddharth Barman , Rachitesh Kumar , Nidhi Rathi

To divide a cake into equal sized pieces most people use a knife and a mixture of luck and dexterity. These attempts are often met with varying success. Through precise geometric constructions performed with the knife replacing Euclid's…

History and Overview · Mathematics 2021-07-13 Alexander Müller-Hermes

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

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 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

A division of a cake by n people is envy free if everyone thinks they got the biggest pieces. Note that peoples tastes can differ. There is a discrete protocol for envy free division for n=3 which takes at most 5 cuts. For n=4 and beyond…

Logic · Mathematics 2015-08-25 William Gasarch

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 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 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 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

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

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 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

The cake-cutting problem involves dividing a heterogeneous, divisible resource fairly between $n$ agents. Br\^{a}nzei et al. [6] introduced {\em generalised cut and choose} (GCC) protocols, a formal model for representing cake-cutting…

Computer Science and Game Theory · Computer Science 2021-08-10 Paul W. Goldberg , Ioana Iaru

Two people meet in a coffeehouse and decide to share one dessert from a menu of several possible choices. How should they choose which one? A method is presented that is intended to be practical, avoiding the need for long negotiations or…

History and Overview · Mathematics 2023-09-19 Tanya Khovanova , Daniel A. Klain

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

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

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 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