Mechanism Design for Extending the Accessibility of Facilities
Hau Chan, Jianan Lin, Chenhao Wang, Yanxi Xie
TL;DR
The paper studies a fixed-facility facility location problem on the real line augmented by an accessibility range $ (a,b) $ with $ |a-b| \le d $, enabling zero-cost travel within the range to improve accessibility without relocating the facility. It defines strategyproof, group-strategyproof, and strong-group-strategyproof mechanisms that choose $ (a,b) $ to approximately minimize the social cost $ SC $ or the maximum cost $ MC $, under two objectives and with both deterministic and randomized considerations. For the social cost, it provides an optimal GSP mechanism and a SGSP mechanism with an $(n-1)$-approximation, along with a lower bound of $ \frac{n+2}{4} $ for any deterministic SGSP mechanism; for the maximum cost, it presents a 2-approximation GSP mechanism with a matching lower bound, and a 2-approximation SGSP mechanism, plus corresponding lower bounds. The paper also proves that randomized SGSP mechanisms cannot surpass the stated deterministic bounds by establishing lower bounds of $ \frac{n+2}{4} $ for $ SC $ and $ 1.5 $ for $ MC $. Overall, the work provides tight deterministic guarantees and fundamental randomized limitations while offering practical insights for deploying continuous accessibility ranges to improve facility accessibility without relocation.
Abstract
We study a variation of facility location problems (FLPs) that aims to improve the accessibility of agents to the facility within the context of mechanism design without money. In such a variation, agents have preferences on the ideal locations of the facility on a real line, and the facility's location is fixed in advance where (re)locating the facility is not possible due to various constraints (e.g., limited space and construction costs). To improve the accessibility of agents to facilities, existing mechanism design literature in FLPs has proposed to structurally modify the real line (e.g., by adding a new interval) or provide shuttle services between two points when structural modifications are not possible. In this paper, we focus on the latter approach and propose to construct an accessibility range to extend the accessibility of the facility. In the range, agents can receive accommodations (e.g., school buses, campus shuttles, or pickup services) to help reach the facility. Therefore, the cost of each agent is the distance from their ideal location to the facility (possibility) through the range. We focus on designing strategyproof mechanisms that elicit true ideal locations from the agents and construct accessibility ranges (intervals) to approximately minimize the social cost or the maximum cost of agents. For both social and maximum costs, we design group strategyproof mechanisms with asymptotically tight bounds on the approximation ratios.