Heterogeneous facility location without money

Serafino, Paolo; Ventre, Carmine

doi:10.1016/j.tcs.2016.04.033

Cited by 49 publications

(42 citation statements)

References 19 publications

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“…The original model [1,30] assumes single-peaked preferences, the obnoxious facility model [7,8,16] assumes singled-dipped (also known as single-caved preferences) whereas the dual preference model [33,34,39] assumes a combination of single-peaked and single-dipped preferences. Each preference structure in these works is motivated by corresponding real-life scenarios; in this light, our model can also be seen as another interesting preference structure, motivated by a different realistic scenario, which immediately places it in tight connection to the related work in artificial intelligence and theoretical computer science.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Preference relations that give rise to such utility structures are referred to as single-dipped or single-caved preferences [25]. Serafino and Ventre [33,34] introduced and studied the setting with heterogeneous facilities, in which agents' locations are known and they declare their interests in different facilities. Building on the idea of heterogeneous facilities, a recent literature [16,39] considers a single facility location setting where the agents report their most preferred positions, along with a binary variable, indicating whether the facility is desirable or obnoxious.…”

Section: Related Work On Facility Locationmentioning

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: Conclusion and Discussionmentioning

confidence: 99%

Section: Related Work On Facility Locationmentioning

confidence: 99%

Facility location with double-peaked preferences

Filos-Ratsikas

Zhang

et al. 2017

Auton Agent Multi-Agent Syst

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show abstract

“…In particular, the most considered problem is the one of facilities location on a line (Procaccia and Tennenholtz 2009; Serafino and Ventre 2016; Serafino and Ventre 2014; Ferraioli, Serafino, and . Much of this literature has focused on identifying verifications which seem natural for a particular application and suffice to design useful mechanisms (Koutsoupias 2014;Serafino and Ventre 2016;Fotakis, Krysta, and Ventre 2014), in contrast to the present work which fixes a set of allocation rules and asks what verification would be minimally necessary to render the mechanisms truthful. Most similarly to our own work, Ferraioli et al (2016) have considered the question the minimum set of assumptions needed in the facility location setting.…”

Section: Related Workmentioning

confidence: 98%

Partial Verification as a Substitute for Money

Ceppi¹,

Kash

Frongillo

2019

AAAI

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Recent work shows that we can use partial verification instead of money to implement truthful mechanisms. In this paper we develop tools to answer the following question. Given an allocation rule that can be made truthful with payments, what is the minimal verification needed to make it truthful without them? Our techniques leverage the geometric relationship between the type space and the set of possible allocations.

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“…The two facilities should be some distance far away due to diversification requirements. Since each agent needs services from both heterogeneous facilities, the cost of each agent should be the sum of his Euclidean distances to the two facilities (Serafino & Ventre, 2014). For Game 2 of the homogeneous two-facility location game, we show an instance that the social planner plans to deploy two temporary COVID-19 testing sites in a street (Kaplan, 2020).…”

Section: Introductionmentioning

confidence: 99%

Two-facility Location Games with Minimum Distance Requirement

Xu¹,

et al. 2021

jair

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We study the mechanism design problem of a social planner for locating two facilities on a line interval [0, 1], where a set of n strategic agents report their locations and a mechanism determines the locations of the two facilities. We consider the requirement of a minimum distance 0 ≤ d ≤ 1 between the two facilities. Given the two facilities are heterogeneous, we model the cost/utility of an agent as the sum of his distances to both facilities. In the heterogeneous two-facility location game to minimize the social cost, we show that the optimal solution can be computed in polynomial time and prove that carefully choosing one optimal solution as output is strategyproof. We also design a strategyproof mechanism minimizing the maximum cost. Given the two facilities are homogeneous, we model the cost/utility of an agent as his distance to the closer facility. In the homogeneous two-facility location game for minimizing the social cost, we show that any deterministic strategyproof mechanism has unbounded approximation ratio. Moreover, in the obnoxious heterogeneous two-facility location game for maximizing the social utility, we propose new deterministic group strategyproof mechanisms with provable approximation ratios and establish a lower bound (7 − d)/6 for any deterministic strategyproof mechanism. We also design a strategyproof mechanism maximizing the minimum utility. In the obnoxious homogeneous two-facility location game for maximizing the social utility, we propose deterministic group strategyproof mechanisms with provable approximation ratios and establish a lower bound 4/3. Besides, in the two-facility location game with triple-preference, where each facility may be favorable, obnoxious, indifferent for any agent, we further motivate agents to report both their locations and preferences towards the two facilities truthfully, and design a deterministic group strategyproof mechanism with an approximation ratio 4.

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Heterogeneous facility location without money

Cited by 49 publications

References 19 publications

Facility location with double-peaked preferences

Facility location with double-peaked preferences

Partial Verification as a Substitute for Money

Two-facility Location Games with Minimum Distance Requirement

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