Truthful facility assignment with resource augmentation: an exact analysis of serial dictatorship

We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space have to be assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the soc...

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Published in:	Mathematical programming Vol. 203; no. 1-2; pp. 901 - 930
Main Authors:	Caragiannis, Ioannis, Filos-Ratsikas, Aris, Frederiksen, Søren Kristoffer Stiil, Hansen, Kristoffer Arnsfelt, Tan, Zihan
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2024 Springer
Subjects:	Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Theoretical 91A68 68W40 Approximation ratio Resource augmentation Mechanism design without money Serial dictatorship 68W25
ISSN:	0025-5610, 1436-4646
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Abstract	We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space have to be assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., the total distance between the most-preferred points of the agents and their corresponding facilities in the assignment, under the constraint of truthfulness, which ensures that agents do not misreport their most-preferred points. We propose a resource augmentation framework , where a truthful mechanism is evaluated by its worst-case performance on an instance with enhanced facility capacities against the optimal mechanism on the same instance with the original capacities. We study a well-known mechanism, Serial Dictatorship, and provide an exact analysis of its performance. Among other results, we prove that Serial Dictatorship has approximation ratio g / ( g - 2 ) when the capacities are multiplied by any integer g ≥ 3 . Our results suggest that with a limited augmentation of the resources we can achieve exponential improvements on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation factor becomes large. We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation.
AbstractList	We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space have to be assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., the total distance between the most-preferred points of the agents and their corresponding facilities in the assignment, under the constraint of truthfulness, which ensures that agents do not misreport their most-preferred points. We propose a resource augmentation framework , where a truthful mechanism is evaluated by its worst-case performance on an instance with enhanced facility capacities against the optimal mechanism on the same instance with the original capacities. We study a well-known mechanism, Serial Dictatorship, and provide an exact analysis of its performance. Among other results, we prove that Serial Dictatorship has approximation ratio $$g/(g-2)$$ g / ( g - 2 ) when the capacities are multiplied by any integer $$g \ge 3$$ g ≥ 3 . Our results suggest that with a limited augmentation of the resources we can achieve exponential improvements on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation factor becomes large. We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation. We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space have to be assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., the total distance between the most-preferred points of the agents and their corresponding facilities in the assignment, under the constraint of truthfulness, which ensures that agents do not misreport their most-preferred points. We propose a resource augmentation framework, where a truthful mechanism is evaluated by its worst-case performance on an instance with enhanced facility capacities against the optimal mechanism on the same instance with the original capacities. We study a well-known mechanism, Serial Dictatorship, and provide an exact analysis of its performance. Among other results, we prove that Serial Dictatorship has approximation ratio [Formula omitted] when the capacities are multiplied by any integer [Formula omitted]. Our results suggest that with a limited augmentation of the resources we can achieve exponential improvements on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation factor becomes large. We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation. We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space have to be assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., the total distance between the most-preferred points of the agents and their corresponding facilities in the assignment, under the constraint of truthfulness, which ensures that agents do not misreport their most-preferred points. We propose a resource augmentation framework , where a truthful mechanism is evaluated by its worst-case performance on an instance with enhanced facility capacities against the optimal mechanism on the same instance with the original capacities. We study a well-known mechanism, Serial Dictatorship, and provide an exact analysis of its performance. Among other results, we prove that Serial Dictatorship has approximation ratio g / ( g - 2 ) when the capacities are multiplied by any integer g ≥ 3 . Our results suggest that with a limited augmentation of the resources we can achieve exponential improvements on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation factor becomes large. We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation.
Audience	Academic
Author	Filos-Ratsikas, Aris Caragiannis, Ioannis Tan, Zihan Frederiksen, Søren Kristoffer Stiil Hansen, Kristoffer Arnsfelt
Author_xml	– sequence: 1 givenname: Ioannis surname: Caragiannis fullname: Caragiannis, Ioannis organization: Department of Computer Science, Aarhus University – sequence: 2 givenname: Aris orcidid: 0000-0001-7868-8114 surname: Filos-Ratsikas fullname: Filos-Ratsikas, Aris email: Aris.Filos-Ratsikas@ed.ac.uk organization: School of Informatics, University of Edinburgh – sequence: 3 givenname: Søren Kristoffer Stiil surname: Frederiksen fullname: Frederiksen, Søren Kristoffer Stiil organization: Department of Computer Science, Aarhus University – sequence: 4 givenname: Kristoffer Arnsfelt surname: Hansen fullname: Hansen, Kristoffer Arnsfelt organization: Department of Computer Science, Aarhus University – sequence: 5 givenname: Zihan surname: Tan fullname: Tan, Zihan organization: DIMACS, Rutgers University
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Cites_doi	10.1016/0304-3975(94)90042-6 10.1017/CBO9780511605864 10.1016/j.artint.2022.103713 10.1007/s00453-019-00565-w 10.1007/s00453-019-00584-7 10.2307/1911681 10.1145/347476.347479 10.1007/s00224-017-9826-1 10.1145/950620.950621 10.1007/s00453-016-0238-4 10.1137/S0895480198342310 10.1145/2786.2793 10.1016/j.artint.2018.07.006 10.1006/jagm.1993.1026 10.1145/1980534.1980538 10.1007/BF01189992 10.1007/s003550050160 10.1145/3434417 10.1137/06067660X 10.1006/jeth.2000.2710 10.1007/s00224-011-9359-y 10.1613/jair.5340 10.1007/s00224-008-9112-3 10.1086/260757 10.2307/2998580 10.1007/s00453-012-9676-9 10.1007/s00453-013-9806-z 10.1145/2542174.2542175 10.1007/978-3-540-78773-0_20 10.1145/3033274.3085115 10.1007/978-3-662-54110-4_19 10.24963/ijcai.2021/589 10.1007/978-3-642-17572-5_26 10.1109/SFFCS.1999.814616 10.1007/978-3-662-44803-8_1 10.1007/978-3-642-16170-4_14 10.1145/1993636.1993716 10.1145/1109557.1109662 10.1007/978-3-319-46882-2_3 10.1007/978-3-319-13129-0_13 10.1007/978-3-540-24592-6_14 10.1007/978-3-662-48350-3_39 10.1609/aaai.v30i1.10032 10.1007/978-3-319-77404-6_5 10.1109/FOCS.2017.53 10.1137/1.9781611973730.70
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Snippet	We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space have to be assigned to facilities... We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space have to be assigned to facilities...
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SubjectTerms	Calculus of Variations and Optimal Control; Optimization Combinatorics Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Theoretical
Title	Truthful facility assignment with resource augmentation: an exact analysis of serial dictatorship
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