Strategy-Proof Mechanisms for Facility Location Games with Many Facilities

Escoffier, Bruno; Gourvès, Laurent; Thắng, Nguyễn Kim; Pascual, Fanny; Spanjaard, Olivier

doi:10.1007/978-3-642-24873-3_6

Cited by 37 publications

(36 citation statements)

References 10 publications

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“…Escoffier at al. [5] proved that in this case, the INVERSELY PROPORTIONAL mechanism is strategyproof and achieves an approximation ratio of (K + 1)/2 for K-Facility Location in general metric spaces. Interestingly, Theorem 7.1 shows that these instances are among the hardest ones for deterministic anonymous mechanisms.…”

Section: Introductionmentioning

confidence: 93%

On the Power of Deterministic Mechanisms for Facility Location Games

Fotakis

Tzamos

2013

Automata, Languages, and Programming

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Abstract. 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, i.e., 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 by deterministic strategyproof mechanisms for the problem of locating 2 facilities on the line to minimize the total connection cost is precisely n − 2. Another rather surprising consequence is that the TWO-EXTREMES mechanism of (Procaccia and Tennenholtz, EC 2009) is the only deterministic anonymous strategyproof mechanism with a bounded approximation ratio for 2-Facility Location on the line. The proof of the characterization employs several new ideas and technical tools, which provide new insights into the behavior of deterministic strategyproof mechanisms for K-Facility Location games, and may be of independent interest. Employing one of these tools, we show that for every K ≥ 3, there do not exist any deterministic anonymous strategyproof mechanisms with a bounded approximation ratio for K-Facility Location on the line, even for simple instances with K + 1 agents. Moreover, building on the characterization for the line, we show that there do not exist any deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location on more general metric spaces, which is true even for simple instances with 3 agents located in a star.

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Section: Introductionmentioning

confidence: 93%

On the Power of Deterministic Mechanisms for Facility Location Games

Fotakis

Tzamos

2013

Automata, Languages, and Programming

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“…The main goal of [30] is the location of a single facility on the real line when agents have single-peaked preferences, and the corresponding bounds shown in Table 1 are from that paper. A series of papers have studied generalizations of the problem to more general metric spaces [1,11,32], multiple facilities [14,23,26,27] or even enhancing strategyproof mechanisms with additional capabilities [21,22]. Most of the related work actually considers the same objectives that we do here, namely the social cost or the maximum cost, with the notable exceptions of the least-squares objective [18], the L p norm of costs [17] or the minimax envy [5].…”

Section: Related Work On Facility Locationmentioning

confidence: 99%

“…Our primary objective is to explore double-peaked preferences in facility location settings similar to the ones studied extensively for single-peaked preferences throughout the years [1,11,14,18,20,23,26,27,30,32]. For that reason, following the literature we assume that the cost functions are the same for all agents and that the cost increases linearly, at the same rate, as the output moves away from the peaks.…”

Section: Introductionmentioning

confidence: 99%

Facility location with double-peaked preferences

Filos-Ratsikas

Zhang

et al. 2017

Auton Agent Multi-Agent Syst

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We study the problem of locating a single facility on a real line based on the reports of self-interested agents, when agents have double-peaked preferences, with the peaks being on opposite sides of their locations. We observe that double-peaked preferences capture reallife scenarios and thus complement the well-studied notion of single-peaked preferences. As a motivating example, assume that the government plans to build a primary school along a street; an agent with single-peaked preferences would prefer having the school built exactly next to her house. However, while that would make it very easy for her children to go to school, it would also introduce several problems, such as noise or parking congestion in the morning. A 5-min walking distance would be sufficiently far for such problems to no longer be much of a factor and at the same time sufficiently close for the school to be easily accessible by the children on foot. There are two positions (symmetrically) in each direction and those would be the agent's two peaks of her double-peaked preference. Motivated by natural scenarios like the one described above, we mainly focus on the case where peaks are equidistant from the agents' locations and discuss how our results extend to more general settings. We show that most of the results for single-peaked preferences do not directly apply to this setting, which makes the problem more challenging. As our main contribution, we present a simple truthfulin-expectation mechanism that achieves an approximation ratio of 1 + b/c for both the social and the maximum cost, where b is the distance of the agent from the peak and c is the minimum cost of an agent. For the latter case, we provide a 3/2 lower bound on the approximation ratio of any truthful-in-expectation mechanism. We also study deterministic mechanisms under some natural conditions, proving lower bounds and approximation guarantees. We prove that among a large class of reasonable strategyproof mechanisms, there is no deterministic mechanism that outperforms our truthful-in-expectation mechanism. In order to obtain this result, we first characterize mechanisms for two agents that satisfy two simple properties; we use the same characterization to prove that no mechanism in this class can be groupstrategyproof.

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“…The main message is that deterministic strategyproof mechanisms can achieve a bounded approximation ratio 1 only if we have at most 2 facilities [Procaccia and Tennenholtz 2009;Fotakis and Tzamos 2013a]. On the other hand, randomized mechanisms are known to achieve better approximation ratios for 2 facilities and also a bounded approximation ratio if we have any number k of facilities and only k + 1 agents [Escoffier et al 2011]. Notably, instances with only k + 1 agents are known to be hard for deterministic mechanisms.…”

Section: The Model and Related Workmentioning

confidence: 99%

Strategyproof facility location with concave costs

Fotakis

Tzamos

2014

SIGecom Exch.

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In k-Facility Location games, n strategic agents report their locations on the real line and a mechanism maps them to k facilities. Each agent seeks to minimize her connection cost to the nearest facility and the mechanism should be strategyproof and approximately efficient. Facility Location games have received considerable attention in the framework of approximate mechanism design without money. In this letter, we discuss some recent positive results on the approximability of k-Facility Location by randomized strategyproof mechanisms. Interestingly, these results hold even if the agents' connection cost is a concave cost function of the distance.

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Strategy-Proof Mechanisms for Facility Location Games with Many Facilities

Cited by 37 publications

References 10 publications

On the Power of Deterministic Mechanisms for Facility Location Games

On the Power of Deterministic Mechanisms for Facility Location Games

Facility location with double-peaked preferences

Strategyproof facility location with concave costs

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