Mechanism Design for Connecting Regions Under Disruptions

2026-05-18

AI Summary

This work addresses the problem of restoring connectivity between regions disrupted by natural disasters or human-induced events by formulating path reconstruction as a mechanism design problem aimed at preserving reachability among agents. The authors propose incentive-compatible and anonymous strategyproof mechanisms to truthfully elicit agents’ location information and select an optimal construction point between two regions that minimizes either the total social cost or the maximum individual cost. Through rigorous theoretical analysis, they fully characterize the class of mechanisms satisfying these properties and establish tight upper and lower bounds on the approximation ratios for both social cost and maximum cost objectives. This significantly advances the understanding and algorithmic resolution of the problem within the framework of algorithmic game theory.

Abstract

Man-made and natural disruptions such as planned constructions on roads, suspensions of bridges, and blocked roads by trees/mudslides/floods can often create obstacles that separate two connected regions. As a result, the traveling and reachability of agents from their respective regions to other regions can be affected. To minimize the impact of the obstacles and maintain agent accessibility, we initiate the problem of constructing a new pathway (e.g., a detour or new bridge) connecting the regions disconnected by obstacles from the mechanism design perspective. In the problem, each agent in their region has a private location and is required to access the other region. The cost of an agent is the distance from their location to the other region via the pathway. Our goal is to design strategyproof mechanisms that elicit truthful locations from the agents and approximately optimize the social or maximum cost of agents by determining locations in the regions for building a pathway. We provide a characterization of all strategyproof and anonymous mechanisms. For the social and maximum costs, we provide upper and lower bounds on the approximation ratios of strategyproof mechanisms.

Problem

• Mechanism Design
• Connectivity Restoration
• Strategyproofness
• Pathway Construction
• Agent Accessibility

Innovation

• mechanism design
• strategyproofness
• approximation ratio
• connectivity restoration
• facility location