Mechanism Design for Extending the Accessibility of Facilities

TL;DR

This paper introduces strategyproof mechanisms for facility accessibility extension via constructed ranges, aiming to minimize agents' travel costs without relocating the facility, applicable in scenarios like shuttle services.

Contribution

It proposes novel group strategyproof mechanisms for constructing accessibility ranges that approximately minimize social and maximum costs in fixed-location facility problems.

Findings

Mechanisms achieve asymptotically tight approximation bounds.

Designed for both social cost and maximum cost minimization.

Applicable to real-world scenarios like shuttle and pickup services.

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.