Waste makes haste: Bounded time protocols for envy-free cake cutting with free disposal

Erel Segal-Halevi; Avinatan Hassidim; Yonatan Aumann

Waste makes haste: Bounded time protocols for envy-free cake cutting with free disposal

Erel Segal-Halevi, Avinatan Hassidim, Yonatan Aumann

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

Abstract

We consider the classic problem of envy-free division of a heterogeneous good (aka the cake) among multiple agents. It is well known that if each agent must receive a contiguous piece then there is no finite protocol for the problem, whenever there are 3 or more agents. This impossibility result, however, assumes that the entire cake must be allocated. In this paper we study the problem in a setting where the protocol may leave some of the cake un-allocated, as long as each agent obtains at least some positive value (according to its valuation). We prove that this version of the problem is solvable in a bounded time. For the case of 3 agents we provide a finite and bounded-time protocol that guarantees each agent a share with value at least 1/3, which is the most that can be guaranteed.

Original language	English
Title of host publication	AAMAS 2015 - Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems
Editors	Edith Elkind, Gerhard Weiss, Pinar Yolum, Rafael H. Bordini
Publisher	International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Pages	901-908
Number of pages	8
ISBN (Electronic)	9781450337700
State	Published - 2015
Event	14th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2015 - Istanbul, Turkey Duration: 4 May 2015 → 8 May 2015

Publication series

Name	Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Volume	2
ISSN (Print)	1548-8403
ISSN (Electronic)	1558-2914

Conference

Conference	14th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2015
Country/Territory	Turkey
City	Istanbul
Period	4/05/15 → 8/05/15

Bibliographical note

Publisher Copyright:
Copyright © 2015, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.

Keywords

Cake-cutting
Envy-free
Fair division
Finite algorithm

Cite this

Segal-Halevi, E., Hassidim, A., & Aumann, Y. (2015). Waste makes haste: Bounded time protocols for envy-free cake cutting with free disposal. In E. Elkind, G. Weiss, P. Yolum, & R. H. Bordini (Eds.), AAMAS 2015 - Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems (pp. 901-908). (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS; Vol. 2). International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).

Segal-Halevi, Erel ; Hassidim, Avinatan ; Aumann, Yonatan. / Waste makes haste : Bounded time protocols for envy-free cake cutting with free disposal. AAMAS 2015 - Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems. editor / Edith Elkind ; Gerhard Weiss ; Pinar Yolum ; Rafael H. Bordini. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), 2015. pp. 901-908 (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS).

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abstract = "We consider the classic problem of envy-free division of a heterogeneous good (aka the cake) among multiple agents. It is well known that if each agent must receive a contiguous piece then there is no finite protocol for the problem, whenever there are 3 or more agents. This impossibility result, however, assumes that the entire cake must be allocated. In this paper we study the problem in a setting where the protocol may leave some of the cake un-allocated, as long as each agent obtains at least some positive value (according to its valuation). We prove that this version of the problem is solvable in a bounded time. For the case of 3 agents we provide a finite and bounded-time protocol that guarantees each agent a share with value at least 1/3, which is the most that can be guaranteed.",

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Segal-Halevi, E, Hassidim, A & Aumann, Y 2015, Waste makes haste: Bounded time protocols for envy-free cake cutting with free disposal. in E Elkind, G Weiss, P Yolum & RH Bordini (eds), AAMAS 2015 - Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems. Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS, vol. 2, International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), pp. 901-908, 14th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2015, Istanbul, Turkey, 4/05/15.

Waste makes haste: Bounded time protocols for envy-free cake cutting with free disposal. / Segal-Halevi, Erel; Hassidim, Avinatan ; Aumann, Yonatan.
AAMAS 2015 - Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems. ed. / Edith Elkind; Gerhard Weiss; Pinar Yolum; Rafael H. Bordini. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS), 2015. p. 901-908 (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Segal-Halevi E, Hassidim A , Aumann Y. Waste makes haste: Bounded time protocols for envy-free cake cutting with free disposal. In Elkind E, Weiss G, Yolum P, Bordini RH, editors, AAMAS 2015 - Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems. International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS). 2015. p. 901-908. (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS).

Waste makes haste: Bounded time protocols for envy-free cake cutting with free disposal

Abstract

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Bibliographical note

Keywords

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Cite this