Asymptotically optimal strategy-proof mechanisms for two-facility games

Lu, Pinyan; Sun, Xiaorui; Wang, Yajun; Zhu, Ziwei

doi:10.1145/1807342.1807393

Cited by 127 publications

(126 citation statements)

References 30 publications

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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%

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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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Section: Related Work On Facility Locationmentioning

confidence: 99%

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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“…Procaccia and Tennenholtz [17] initiated the study of approximate mechanism design without payments for combinatorial problems by studying facility location problems. Their studies triggered several follow-up articles on this topic (see, e.g., [1,13,12,6,7]). Dughmi and Gosh [4] derived approximate mechanisms without money for several variants of the assignment problems.…”

Section: Binding Reportsmentioning

confidence: 99%

Mechanisms for Hiring a Matroid Base without Money

Pountourakis

Schäfer

2014

Algorithmic Game Theory

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Abstract. We consider the problem of designing mechanisms for hiring a matroid base without money. In our model, the elements of a given matroid correspond to agents who might misreport their actual costs that are incurred if they are hired. The goal is to hire a matroid base of minimum total cost. There are no monetary transfers involved. We assume that the reports are binding in the sense that an agent's cost is equal to the maximum of his declared and actual costs. Our model encompasses a variety of problems as special cases, such as computing a minimum cost spanning tree or finding minimum cost allocation of jobs to machines. We derive a polynomial-time randomized mechanism that is truthful in expectation and achieves an approximation ratio of (m − r)/2 + 1, where m and r refer to the number of elements and the rank of the matroid, respectively. We also prove that this is best possible by showing that no mechanism that is truthful in expectation can achieve a better approximation ratio in general. If the declared costs of the agents are bounded by the cost of a socially optimal solution, we are able derive an improved approximation ratio of 3 √ m. For example, this condition is satisfied if the costs constitute a metric in the graphical matroid. Our mechanism iteratively extends a partial solution by adding feasible elements at random. As it turns out, this algorithm achieves the best possible approximation ratio if it is equipped with a distribution that is optimal for the allocation of a single task to multiple machines. This seems surprising given that matroids allow for much richer combinatorial structures than the assignment of a single job.

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“…The second facility is placed at x j − max{d l , 2d r }, if d l > d r , and to x j + max{d r , 2d l }, otherwise. DICTATORIAL is an adaptation of the mechanism of [10] for the circle. As in [10,Section 5], it can be shown that DICTATORIAL is strategyproof and (n − 1)-approximate for the line.…”

Section: Strategyproof Mechanisms For 2-facility Location: Outlinementioning

confidence: 99%

“…Next, we employ the notion of partial group strategyproofness [10,Section 3], and a new technical tool for moving agents between different coalitions without affecting the mechanism's outcome (Lemma 5.1), and show that any nice mechanism applied to 3-location instances with n ≥ 5 agents either admits a (full) dictator, or places the facilities at the two extremes (Theorem 3.3). Rather surprisingly, this implies that nice mechanisms for 3 agents are somewhat less restricted than nice mechanisms for n ≥ 5 agents.…”

Section: Introductionmentioning

confidence: 99%

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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Asymptotically optimal strategy-proof mechanisms for two-facility games

Cited by 127 publications

References 30 publications

Facility location with double-peaked preferences

Facility location with double-peaked preferences

Mechanisms for Hiring a Matroid Base without Money

On the Power of Deterministic Mechanisms for Facility Location Games

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