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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Veröffentlicht in:Mathematical programming Jg. 203; H. 1-2; S. 901 - 930
Hauptverfasser: Caragiannis, Ioannis, Filos-Ratsikas, Aris, Frederiksen, Søren Kristoffer Stiil, Hansen, Kristoffer Arnsfelt, Tan, Zihan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2024
Springer
Schlagworte:
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
Online-Zugang:Volltext
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Zusammenfassung: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.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-022-01902-8