Mechanism design on discrete lines and cycles

Dokow, Elad; Feldman, Michal; Meir, Reshef; Nehama, Ilan

doi:10.1145/2229012.2229045

Cited by 58 publications

(50 citation statements)

References 24 publications

(37 reference statements)

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“…Schummer and Vohra [17] extended this characterization to tree metrics, and proved that for non-tree metrics, any onto strategyproof mechanism must be a dictatorship. More recently, Dokow et al [3] obtained similar characterizations for locating a single facility on the discrete line and on the discrete circle.…”

Section: Introductionmentioning

confidence: 88%

Strategyproof Facility Location for Concave Cost Functions

Fotakis

Tzamos

2015

Algorithmica

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Abstract. We consider k-Facility Location games, where n strategic agents report their locations on the real line, and a mechanism maps them to k facilities. Each agent seeks to minimize his connection cost, given by a nonnegative increasing function of his distance to the nearest facility. Departing from previous work, that mostly considers the identity cost function, we are interested in mechanisms without payments that are (group) strategyproof for any given cost function, and achieve a good approximation ratio for the social cost and/or the maximum cost of the agents. We present a randomized mechanism, called EQUAL COST, which is group strategyproof and achieves a bounded approximation ratio for all k and n, for any given concave cost function. The approximation ratio is at most 2 for MAX COST and at most n for SOCIAL COST. To the best of our knowledge, this is the first mechanism with a bounded approximation ratio for instances with k ≥ 3 facilities and any number of agents. Our result implies an interesting separation between deterministic mechanisms, whose approximation ratio for MAX COST jumps from 2 to unbounded when k increases from 2 to 3, and randomized mechanisms, whose approximation ratio remains at most 2 for all k. On the negative side, we exclude the possibility of a mechanism with the properties of EQUAL COST for strictly convex cost functions. We also present a randomized mechanism, called PICK THE LOSER, which applies to instances with k facilities and only n = k + 1 agents. For any given concave cost function, PICK THE LOSER is strongly group strategyproof and achieves an approximation ratio of 2 for SOCIAL COST.

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Section: Introductionmentioning

confidence: 88%

Strategyproof Facility Location for Concave Cost Functions

Fotakis

Tzamos

2015

Algorithmica

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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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“…Then, we consider the instance x ′′ = (x ′ −4 , l). Since F is anonymous 4 and strategyproof, and since l ∈ F (x ′ ), x ′′ 3 = l ∈ F (x ′′ ). Moreover, by Proposition 2.4, x ′′ 4 = l + ε ∈ F (x ′′ ), because for the (1|2|3, 4)-well-separated instance x, F 3 (x) = x 4 , and x ′′ is an (1|2|3, 4)-well-separated instance with x ′′ 4 ≤ x 4 .…”

Section: Inexistence Of Anonymous Nice Mechanisms For More Than 2 Facmentioning

confidence: 99%

“…As in Section 5, we first extend the characterization to 3-agent instances, and then use partial group strategyproofness to further 4 We highlight that the agents 3 and 4 implicitly switch indices in x ′ and x ′′ . More specifically, since we require that the agents are arranged on the line in increasing order of their indices, the location of agent 3 is l + ε in x ′ and l in x ′′ , and the location of agent 4 is 3λ 2 + λ + 1 in x ′ and l + ε in x ′′ .…”

Section: Inexistence Of Nice Mechanisms For 2-facility Location In Momentioning

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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Mechanism design on discrete lines and cycles

Cited by 58 publications

References 24 publications

Strategyproof Facility Location for Concave Cost Functions

Strategyproof Facility Location for Concave Cost Functions

Facility location with double-peaked preferences

On the Power of Deterministic Mechanisms for Facility Location Games

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