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Related papers: Online Cake Cutting

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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 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…

Combinatorics · Mathematics 2017-10-16 Roberto Barrera , Kathryn Nyman , Amanda Ruiz , Francis Edward Su , Yan X. Zhang

We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works,…

Computer Science and Game Theory · Computer Science 2020-09-15 Xiaohui Bei , Guangda Huzhang , Warut Suksompong

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

In this paper, we consider the classic fair division problem of allocating $m$ divisible items to $n$ agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the…

Computer Science and Game Theory · Computer Science 2024-11-18 Yannan Bai , Kamesh Munagala , Yiheng Shen , Ian Zhang

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

We study the envy-free cake-cutting problem for $d+1$ players with $d$ cuts, for both the oracle function model and the polynomial time function model. For the former, we derive a $\theta(({1\over\epsilon})^{d-1})$ time matching bound for…

Computer Science and Game Theory · Computer Science 2009-07-10 Xiaotie Deng , Qi Qi , Amin Saberi

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

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

We consider fair division problems where indivisible items arrive one-by-one in an online fashion and are allocated immediately to agents who have additive utilities over these items. Many existing offline mechanisms do not work in this…

Computer Science and Game Theory · Computer Science 2020-06-30 Martin Aleksandrov , Toby Walsh

This paper combines two key ingredients for online algorithms - competitive analysis (e.g. the competitive ratio) and advice complexity (e.g. the number of advice bits needed to improve online decisions) - in the context of a simple online…

Computer Science and Game Theory · Computer Science 2020-06-30 Martin Aleksandrov , Toby Walsh

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 problem of fair cake-cutting where each agent receives a connected piece of the cake. A division of the cake is deemed fair if it is equitable, which means that all agents derive the same value from their assigned piece. Prior…

Computer Science and Game Theory · Computer Science 2024-12-19 Umang Bhaskar , A. R. Sricharan , Rohit Vaish

In this paper, we show algorithms for solving the cake-cutting problem in sublinear-time. More specifically, we preassign (simple) fair portions to o(n) players in o(n)-time, and minimize the damage to the rest of the players. All currently…

Data Structures and Algorithms · Computer Science 2015-07-24 Hiro Ito , Takahiro Ueda

Behavioural economists have shown that people are often averse to inequality and will make choices to avoid unequal outcomes. In this paper, we consider how to allocate indivisible goods fairly so as to minimize inequality. We consider how…

Computer Science and Game Theory · Computer Science 2018-10-15 Martin Aleksandrov , Cunjing Ge , Toby Walsh

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

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

We consider the problem of envy-free cake cutting, which is the distribution of a continuous heterogeneous resource among self interested players such that nobody prefers what somebody else receives to what they get. Existing work has…

Computer Science and Game Theory · Computer Science 2018-01-26 Eshwar Ram Arunachaleswaran , Ragavendran Gopalakrishnan

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

We consider a practically motivated variant of the canonical online fair allocation problem: a decision-maker has a budget of perishable resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and…

Optimization and Control · Mathematics 2026-04-03 Siddhartha Banerjee , Chamsi Hssaine , Sean R. Sinclair