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Related papers: Disproportionate division

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The fair division literature in economics considers how to divide resources between multiple agents such that the allocation is envy-free: each agent receives their favorite piece. Researchers have developed a variety of fair division…

Programming Languages · Computer Science 2023-04-11 Noah Bertram , Alex Levinson , Justin Hsu

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

Envy-free cake-cutting protocols procedurally divide an infinitely divisible good among a set of agents so that no agent prefers another's allocation to their own. These protocols are highly complex and difficult to prove correct. Recently,…

Computer Science and Game Theory · Computer Science 2024-05-31 Noah Bertram , Tean Lai , Justin Hsu

We consider a classical envy-free cake cutting problem. The first limited protocol was proposed by Aziz and McKenzie in 2016 arXiv:1604.03655. The disadvantage of this protocol is its high complexity. The authors proved that the maximum…

Computational Complexity · Computer Science 2023-06-07 Georgy Sokolov

This paper extends the classic cake-cutting problem to a situation in which the "cake" is divided among families. Each piece of cake is owned and used simultaneously by all members of the family. A typical example of such a cake is land. We…

Computer Science and Game Theory · Computer Science 2019-08-12 Erel Segal-Halevi , Shmuel Nitzan

We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under…

Combinatorics · Mathematics 2023-11-16 Alexandr Grebennikov , Xenia Isaeva , Andrei V. Malyutin , Mikhail Mikhailov , Oleg R. Musin

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 study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show…

Computer Science and Game Theory · Computer Science 2017-05-19 Vijay Menon , Kate Larson

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

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

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 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

Consider n straight line cuts of a circular pizza made so as to maximize the number of pieces. We investigate how fair such a maximal division may be and how many slices are obtained if the cuts are successfully made with a certain…

Probability · Mathematics 2007-05-23 Floyd E. Brown , Anant P. Godbole

We study the problem of dividing a multi-layered cake under non-overlapping constraints. This problem, recently proposed by Hosseini et al. (IJCAI, 2020), captures several natural scenarios such as the allocation of multiple facilities over…

Computer Science and Game Theory · Computer Science 2022-12-22 Ayumi Igarashi , Frédéric Meunier

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework…

Computer Science and Game Theory · Computer Science 2017-06-07 Sylvain Bouveret , Katarína Cechlárová , Edith Elkind , Ayumi Igarashi , Dominik Peters

The paper considers fair allocation of indivisible nondisposable items that generate disutility (chores). We assume that these items are placed in the vertices of a graph and each agent's share has to form a connected subgraph of this…

Artificial Intelligence · Computer Science 2018-12-06 Sylvain Bouveret , Katarína Cechlárová , Julien Lesca

Austin's moving knife procedure was originally introduced to find a consensus division of an interval/circular cake between two agents, each of whom believes that they receive exactly half of the cake. We generalise this in two ways: we…

Combinatorics · Mathematics 2025-09-26 Josef Hanke , Ana Rita Pires

We consider the problem of fair allocation of $m$ indivisible items to a group of $n$ agents with subsidy (money). Our work mainly focuses on the allocation of chores but most of our results extend to the allocation of goods as well. We…

Computer Science and Game Theory · Computer Science 2023-07-11 Xiaowei Wu , Cong Zhang , Shengwei Zhou

We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which…

Computer Science and Game Theory · Computer Science 2020-01-01 Erel Segal-Halevi , Warut Suksompong

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
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