Related papers: On the Complexity of Envy-Free Cake Cutting
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…
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…
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…
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…
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…
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…
We study the query complexity of cake cutting and give lower and upper bounds for computing approximately envy-free, perfect, and equitable allocations with the minimum number of cuts. The lower bounds are tight for computing connected…
We consider the well-studied cake cutting problem in which the goal is to find an envy-free allocation based on queries from $n$ agents. The problem has received attention in computer science, mathematics, and economics. It has been a major…
We study the discrete variation of the classical cake-cutting problem where n players divide a 1-dimensional cake with exactly (n-1) cuts, replacing the continuous, infinitely divisible "cake" with a necklace of discrete, indivisible…
We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in…
We consider the classic cake-cutting problem of producing envy-free allocations, restricted to the case of four agents. The problem asks for a partition of the cake to four agents, so that every agent finds her piece at least as valuable as…
In the classic problem of fair cake-cutting, a single interval ("cake") has to be divided among n agents with different value measures, giving each agent a single sub-interval with a value of at least 1/n of the total. This paper studies a…
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…
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.…
Relying on configuration spaces and equivariant topology, we study a general "cooperative envy-free division problem". A group of players want to cut a "cake" $I=[0,1]$ and divide among themselves the pieces in an envy-free manner. Once the…
Cake cutting is a classic fair division problem, with the cake serving as a metaphor for a heterogeneous divisible resource. Recently, it was shown that for any number of players with arbitrary preferences over a cake, it is possible to…
The problem of fair division known as "cake cutting" has been the focus of multiple papers spanning several decades. The most prominent problem in this line of work has been to bound the query complexity of computing an envy-free outcome in…
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…
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…
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…