Assigning Agents to a Line

Jens Leth Hougaard, Juan D. Moreno-Ternero, Lars Peter Østerdal

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

We consider the problem of assigning agents to slots on a line, where only one agent can be served at a slot and each agent prefers to be served as close as possible to his target. Our focus is on aggregate gap minimizing methods, i.e., those that minimize the total gap between targets and assigned slots. We first consider deterministic assignment of agents to slots, and provide a direct method for testing if a given deterministic assignment is aggregate gap minimizing. We then consider probabilistic assignment of agents to slots, and make use of the previous method to propose an aggregate gap minimizing modification of the classic random priority method to solve this class of problems. We also provide some logical relations in our setting among standard axioms in the literature on assignment problems, and explore the robustness of our results to several extensions of our setting.
Original languageEnglish
JournalGames and Economic Behavior
Volume87
Pages (from-to)539–553
ISSN0899-8256
DOIs
Publication statusPublished - Sep 2014
Externally publishedYes

Keywords

  • Probabilistic assignment
  • Random priority
  • Aggregate gap minimizing
  • sd-efficiency
  • Bottleneck

Cite this

Hougaard, Jens Leth ; Moreno-Ternero, Juan D. ; Østerdal, Lars Peter. / Assigning Agents to a Line. In: Games and Economic Behavior. 2014 ; Vol. 87. pp. 539–553.
@article{adb3c8b22c82400087a8016806de2eee,
title = "Assigning Agents to a Line",
abstract = "We consider the problem of assigning agents to slots on a line, where only one agent can be served at a slot and each agent prefers to be served as close as possible to his target. Our focus is on aggregate gap minimizing methods, i.e., those that minimize the total gap between targets and assigned slots. We first consider deterministic assignment of agents to slots, and provide a direct method for testing if a given deterministic assignment is aggregate gap minimizing. We then consider probabilistic assignment of agents to slots, and make use of the previous method to propose an aggregate gap minimizing modification of the classic random priority method to solve this class of problems. We also provide some logical relations in our setting among standard axioms in the literature on assignment problems, and explore the robustness of our results to several extensions of our setting.",
keywords = "Probabilistic assignment, Random priority, Aggregate gap minimizing, sd-efficiency, Bottleneck, Probabilistic assignment, Random priority, Aggregate gap minimizing, sd-efficiency, Bottleneck",
author = "Hougaard, {Jens Leth} and Moreno-Ternero, {Juan D.} and {\O}sterdal, {Lars Peter}",
year = "2014",
month = "9",
doi = "10.1016/j.geb.2014.02.011",
language = "English",
volume = "87",
pages = "539–553",
journal = "Games and Economic Behavior",
issn = "0899-8256",
publisher = "Academic Press",

}

Assigning Agents to a Line. / Hougaard, Jens Leth; Moreno-Ternero, Juan D.; Østerdal, Lars Peter.

In: Games and Economic Behavior, Vol. 87, 09.2014, p. 539–553.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Assigning Agents to a Line

AU - Hougaard, Jens Leth

AU - Moreno-Ternero, Juan D.

AU - Østerdal, Lars Peter

PY - 2014/9

Y1 - 2014/9

N2 - We consider the problem of assigning agents to slots on a line, where only one agent can be served at a slot and each agent prefers to be served as close as possible to his target. Our focus is on aggregate gap minimizing methods, i.e., those that minimize the total gap between targets and assigned slots. We first consider deterministic assignment of agents to slots, and provide a direct method for testing if a given deterministic assignment is aggregate gap minimizing. We then consider probabilistic assignment of agents to slots, and make use of the previous method to propose an aggregate gap minimizing modification of the classic random priority method to solve this class of problems. We also provide some logical relations in our setting among standard axioms in the literature on assignment problems, and explore the robustness of our results to several extensions of our setting.

AB - We consider the problem of assigning agents to slots on a line, where only one agent can be served at a slot and each agent prefers to be served as close as possible to his target. Our focus is on aggregate gap minimizing methods, i.e., those that minimize the total gap between targets and assigned slots. We first consider deterministic assignment of agents to slots, and provide a direct method for testing if a given deterministic assignment is aggregate gap minimizing. We then consider probabilistic assignment of agents to slots, and make use of the previous method to propose an aggregate gap minimizing modification of the classic random priority method to solve this class of problems. We also provide some logical relations in our setting among standard axioms in the literature on assignment problems, and explore the robustness of our results to several extensions of our setting.

KW - Probabilistic assignment

KW - Random priority

KW - Aggregate gap minimizing

KW - sd-efficiency

KW - Bottleneck

KW - Probabilistic assignment

KW - Random priority

KW - Aggregate gap minimizing

KW - sd-efficiency

KW - Bottleneck

UR - https://sfx-45cbs.hosted.exlibrisgroup.com/45cbs?url_ver=Z39.88-2004&url_ctx_fmt=info:ofi/fmt:kev:mtx:ctx&ctx_enc=info:ofi/enc:UTF-8&ctx_ver=Z39.88-2004&rfr_id=info:sid/sfxit.com:azlist&sfx.ignore_date_threshold=1&rft.object_id=954922649140&rft.object_portfolio_id=&svc.holdings=yes&svc.fulltext=yes

U2 - 10.1016/j.geb.2014.02.011

DO - 10.1016/j.geb.2014.02.011

M3 - Journal article

VL - 87

SP - 539

EP - 553

JO - Games and Economic Behavior

JF - Games and Economic Behavior

SN - 0899-8256

ER -