Facility Location with Double-Peaked Preferences

Abstract

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 real-life scenarios and thus complement the well-studied notion of single-peaked preferences. 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; this makes the problem essentially more challenging. As our main contribution, we present a simple truthful-in-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 mechanisms, there is no deterministic mechanism that outpeforms our truthful-in-expectation mechanism.

Heterogeneous Facility Location with Limited Resources

“…In their setting, the facilities are strategic and need to be compensated monetarily in order for them to be built; the goal is to maximize an aggregate objective given that the total payment is below a predefined budget. Besides these works, there is long literature of (homogeneous) facility location, studying different objectives (Alon et al 2010;Cai, Filos-Ratsikas, and Tang 2016;Feigenbaum, Sethuraman, and Ye 2013;Feldman and Wilf 2013), multiple facilities (Escoffier et al 2011;Fotakis and Tzamos 2013;Lu, Wang, and Zhou 2009;Lu et al 2010), different domains (Schummer and Vohra 2002;Tang, Yu, and Zhao 2020;Sui, Boutilier, and Sandholm 2013;Sui and Boutilier 2015), different cost functions (Filos-Ratsikas et al 2015;Fotakis and Tzamos 2016), and several interesting variants (Golomb and Tzamos 2017;Kyropoulou, Ventre, and Zhang 2019;Zhang and Li 2014;Filos-Ratsikas and Voudouris 2021). The very recent survey of Chan et al (2021) provides an excellent overview of the literature on mechanism design for facility location problems and the survey of Anshelevich et al (2021) provides an overview of the literature on distortion, which has been applied for analyzing facility location settings.…”

Facility Reallocation on the Line

“…Moreover, [25] study the two facility problem where the cost function may differ between agents. The paper [9] studies strategy-proof mechanisms for double-peaked preferences, which can model e.g., a scenario where each agent would like to be close to a facility, but not too close. In [24] the trade-off is studied between variance and approximation factor for strategy-proof mechanisms.…”

False-Name-Proof Locations of Two Facilities: Economic and Algorithmic Approaches

“…Moreover, many researches including (Procaccia and Tennenholtz 2013) and (Alon et al 2010) are interested in analyzing the approximation ratios of strategy-proof mechanisms for one or more facilities on a line, a circle, and trees. More recently, locating heterogeneous facilities, i.e., each facility is served for different purpose (Serafino and Ventre 2015), and a single facility location problem with dual preferences, where some agents prefer to stay close to the facility and the others prefer to stay away from (Zou and Li 2015), and with double-peaked preferences, i.e., staying too close to the facility also reduces agents' utility (Filos-Ratsikas et al 2015), are much interested.…”