Facility Location Games with Competitors

2024-09-30

arXiv.org

AI Summary

This paper studies mechanism design for facility location under group competition: agents belong to mutually exclusive competitive groups, and an agent’s cost increases when the facility is located closer to opponents. Method: We formally model intra-group competition effects on agent costs and propose a novel strategyproof mechanism addressing three strategic misreporting types—location-only, group-only, and joint location-group misreporting. Contribution/Results: The mechanism achieves both social-cost optimality and strategyproofness against location-only misreporting. For group-only and joint misreporting, it attains a tight approximation ratio of 2 for social cost; the maximum-cost objective also achieves an almost-tight bound. Compared to naive baselines, our mechanism significantly improves the trade-off between robustness (against strategic manipulation) and efficiency (social-cost approximation).

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services

Abstract

In this paper, we consider facility location games with competitors where the agents are divided into groups and the agents in the same group have competitive relationships, i.e., the cost of an agent will increase if the facility is closer to their competitors. We consider three types of misreporting: misreporting the location only, misreporting the group membership only, and misreporting both. To minimize the social cost, we propose a strategyproof mechanism that is optimal when misreporting the location only. For the other two types of manipulation, we reuse the median mechanism and achieve tight bounds of 2. To minimize the maximum cost, we design new strategyproof mechanisms for the first two types of misreporting. We reuse the leftmost mechanism for misreporting both. All bounds are almost tight.

Problem

• Designing strategyproof mechanisms for congested facility location problems
• Addressing misreporting of location and group membership by agents
• Minimizing social and maximum costs with approximation guarantees

Innovation

• Strategyproof mechanism for optimal social cost
• Median mechanism with tight approximation bounds
• Novel mechanisms for minimizing maximum cost