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On the Power of Deterministic Mechanisms for Facility Location Games

On the Power of Deterministic Mechanisms for Facility Location Games On the Power of Deterministic Mechanisms for Facility Location Games DIMITRIS FOTAKIS, National Technical University of Athens CHRISTOS TZAMOS, Massachusetts Institute of Technology We consider K-Facility Location games, where n strategic agents report their locations in a metric space and a mechanism maps them to K facilities. The agents seek to minimize their connection cost, namely the distance of their true location to the nearest facility, and may misreport their location. We are interested in deterministic mechanisms that are strategyproof, that is, ensure that no agent can benefit from misreporting her location, do not resort to monetary transfers, and achieve a bounded approximation ratio to the total connection cost of the agents (or to the Lp norm of the connection costs, for some p [1, ) or for p = ). Our main result is an elegant characterization of deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location on the line. In particular, we show that for instances with n 5 agents, any such mechanism either admits a unique dictator or always places the facilities at the leftmost and the rightmost location of the instance. As a corollary, we obtain that the best approximation ratio achievable http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Economics and Computation Association for Computing Machinery

On the Power of Deterministic Mechanisms for Facility Location Games

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References (30)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 by ACM Inc.
ISSN
2167-8375
DOI
10.1145/2665005
Publisher site
See Article on Publisher Site

Abstract

On the Power of Deterministic Mechanisms for Facility Location Games DIMITRIS FOTAKIS, National Technical University of Athens CHRISTOS TZAMOS, Massachusetts Institute of Technology We consider K-Facility Location games, where n strategic agents report their locations in a metric space and a mechanism maps them to K facilities. The agents seek to minimize their connection cost, namely the distance of their true location to the nearest facility, and may misreport their location. We are interested in deterministic mechanisms that are strategyproof, that is, ensure that no agent can benefit from misreporting her location, do not resort to monetary transfers, and achieve a bounded approximation ratio to the total connection cost of the agents (or to the Lp norm of the connection costs, for some p [1, ) or for p = ). Our main result is an elegant characterization of deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location on the line. In particular, we show that for instances with n 5 agents, any such mechanism either admits a unique dictator or always places the facilities at the leftmost and the rightmost location of the instance. As a corollary, we obtain that the best approximation ratio achievable

Journal

ACM Transactions on Economics and ComputationAssociation for Computing Machinery

Published: Oct 28, 2014

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