Internet and Network Economics

Volume 6484 of the series Lecture Notes in Computer Science pp 531-538

On (Group) Strategy-Proof Mechanisms without Payment for Facility Location Games

  • Nguyen Kim ThangAffiliated withLAMSADE, CNRS FRE 3234, Université de Paris-DauphineDepartment of Computer Science, University of Aarhus

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We characterize the performance of strategyproof and group-strategyproof social choice rules, for placing a facility on the nodes of a metric network inhabited by N autonomous self-interested agents. Every agent owns a set of locations and caters to minimization of its cost which is the total distance from the facility to its locations. Agents may misreport their locations, so as to manipulate the outcome. A central authority has a set of allowable locations where the facility could be opened. The authority must devise a mechanism that, given the agents reports, places the facility in an allowable location that minimizes the utilitarian social cost — the sum of agents costs. A mechanism is strategyproof (SP) if no agent may misreport its locations and be better off; it is group-strategyproof (GSP) if no coalition of agents benefits by jointly misreporting their locations The requirement for (G)SP in this setting makes optimum placement of the facility impossible and, therefore, we consider approximation (G)SP mechanisms.

For SP mechanisms, we give a simple 3-approximation randomized mechanism and also provide asymptotic lower bounds for different variants. For GSP mechanisms, a (2N + 1)-approximation deterministic GSP mechanism is devised. Although the mechanism is simple, we showed that it is asymptotically optimal up to a constant. Our Ω(N 1 − ε ) lower bound that randomization cannot improve over the approximation factor achieved by the deterministic mechanism, when GSP is required.