scholarly journals Cake cutting: Explicit examples for impossibility results

2019 ◽  
Vol 102 ◽  
pp. 68-72
Author(s):  
Guillaume Chèze
Keyword(s):  
Impossibility Results ◽  
Cake Cutting

scholarly journals Truthful fair division without free disposal

2020 ◽  
Vol 55 (3) ◽  
pp. 523-545 ◽  
Author(s):  
Xiaohui Bei ◽  
Guangda Huzhang ◽  
Warut Suksompong
Keyword(s):  
Fair Division ◽  
Multiple Agents ◽  
Two Agents ◽  
Free Disposal ◽  
Cake Cutting ◽  
Strategic Agents ◽  
Additional Constraints

Abstract 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, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

Fair cake-cutting for imitative agents

2021 ◽  
Author(s):  
Eleonora Cresto ◽  
Diego Tajer
Keyword(s):  
Cake Cutting

Impossibility Results for Rational Belief

Noûs ◽  
2017 ◽  
Vol 53 (1) ◽  
pp. 134-159 ◽  
Author(s):  
Gerhard Schurz
Keyword(s):  
Rational Belief ◽  
Impossibility Results

scholarly journals Preferences Single-Peaked on a Circle

2020 ◽  
Vol 68 ◽  
pp. 463-502 ◽  
Author(s):  
Dominik Peters ◽  
Martin Lackner
Keyword(s):  
Polynomial Time ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Recognition Algorithm ◽  
Approval Voting ◽  
Voting Rules ◽  
One Dimensional ◽  
Facility Location Problems ◽  
Impossibility Results ◽  
Fast Recognition

We introduce the domain of preferences that are single-peaked on a circle, which is a generalization of the well-studied single-peaked domain. This preference restriction is useful, e.g., for scheduling decisions, certain facility location problems, and for one-dimensional decisions in the presence of extremist preferences. We give a fast recognition algorithm of this domain, provide a characterisation by finitely many forbidden subprofiles, and show that many popular single- and multi-winner voting rules are polynomial-time computable on this domain. In particular, we prove that Proportional Approval Voting can be computed in polynomial time for profiles that are single-peaked on a circle. In contrast, Kemeny's rule remains hard to evaluate, and several impossibility results from social choice theory can be proved using only profiles in this domain.

scholarly journals Deterministic, Strategyproof, and Fair Cake Cutting

2017 ◽  
Author(s):  
Vijay Menon ◽  
Kate Larson
Keyword(s):  
Mechanism Design ◽  
Impossibility Result ◽  
Restricted Class ◽  
Piecewise Constant ◽  
Incentive Compatible ◽  
Negative Results ◽  
Cake Cutting ◽  
Design Perspective ◽  
A Minor ◽  
Cutting Problem

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 that for even the restricted class of piecewise constant valuations there exists no direct-revelation mechanism that is strategyproof and even approximately proportional. Subsequently, we remove the non-wasteful constraint and show another impossibility result stating that there is no strategyproof and approximately proportional direct-revelation mechanism that outputs contiguous allocations, again, for even the restricted class of piecewise constant valuations. In addition to the above results, we also present some negative results when considering an approximate notion of strategyproofness, show a connection between direct-revelation mechanisms and mechanisms in the Robertson-Webb model when agents have piecewise constant valuations, and finally also present a (minor) modification to the well-known Even-Paz algorithm that has better incentive-compatible properties for the cases when there are two or three agents.

scholarly journals Cake Cutting: Envy and Truth

2017 ◽  
Author(s):  
Xiaohui Bei ◽  
Ning Chen ◽  
Guangda Huzhang ◽  
Biaoshuai Tao ◽  
Jiajun Wu
Keyword(s):  
Nash Equilibrium ◽  
Private Information ◽  
General Setting ◽  
Impossibility Result ◽  
Market Model ◽  
Truth Telling ◽  
Piecewise Constant ◽  
Cake Cutting ◽  
Strategic Agents ◽  
To Receive

We study envy-free cake cutting with strategic agents, where each agent may manipulate his private information in order to receive a better allocation. We focus on piecewise constant utility functions and consider two scenarios: the general setting without any restriction on the allocations and the restricted setting where each agent has to receive a connected piece. We show that no deterministic truthful envy-free mechanism exists in the connected piece scenario, and the same impossibility result for the general setting with some additional mild assumptions on the allocations. Finally, we study a large market model where the economy is replicated and demonstrate that truth-telling converges to a Nash equilibrium.

scholarly journals Monotonicity and competitive equilibrium in cake-cutting

2018 ◽  
Vol 68 (2) ◽  
pp. 363-401 ◽  
Author(s):  
Erel Segal-Halevi ◽  
Balázs R. Sziklai
Keyword(s):  
Competitive Equilibrium ◽  
Cake Cutting
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