Fair multi-cake cutting

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.

Download Full-text

Fair cake-cutting for imitative agents

Social Choice and Welfare ◽

10.1007/s00355-021-01375-2 ◽

2021 ◽

Author(s):

Eleonora Cresto ◽

Diego Tajer

Keyword(s):

Cake Cutting

Download Full-text

Deterministic, Strategyproof, and Fair Cake Cutting

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/50 ◽

2017 ◽

Cited By ~ 3

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.

Download Full-text

Cake Cutting: Envy and Truth

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/507 ◽

2017 ◽

Cited By ~ 4

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.

Download Full-text