Approximately Optimal Mechanisms for Strategyproof Facility Location: Minimizing $L_p$ Norm of Costs

Feigenbaum, Itai; Sethuraman, Jay; Yuan, Chun

doi:10.48550/arxiv.1305.2446

Cited by 2 publications

(2 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A property that requires special mention is that of position invariance, which is a very natural property as discussed in the introduction. This property was independently defined by [10] where it was referred to as shift invariance. One can view position invariance as an analogue to neutrality in problems like the one studied here, where there is a continuum of outcomes instead of a finite set.…”

Section: Preliminariesmentioning

confidence: 99%

Facility location with double-peaked preferences

Filos-Ratsikas

Zhang

et al. 2017

Auton Agent Multi-Agent Syst

View full text Add to dashboard Cite

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.

show abstract

Section: Preliminariesmentioning

confidence: 99%

Facility location with double-peaked preferences

Filos-Ratsikas

Zhang

et al. 2017

Auton Agent Multi-Agent Syst

View full text Add to dashboard Cite

show abstract

“…A property that requires special mention is that of position invariance, which is a very natural property as discussed in the introduction. This property was independently defined by (Feigenbaum, Sethuraman, and Ye 2013) where it was referred to as shift invariance. One can view position invariance as an analogue to neutrality in problems like the one studied here, where there is a continuum of outcomes instead of a finite set.…”

Section: Preliminariesmentioning

confidence: 99%