On the Power of Deterministic Mechanisms for Facility Location Games

• Published in: Automata, Languages, and Programming pp. 449 - 460
• Main Authors: Fotakis, Dimitris, Tzamos, Christos
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2013
• Series: Lecture Notes in Computer Science
• Subjects: Approximation Ratio; Deterministic Mechanism; General Metrics; Prefer Agent; Social Choice
• ISBN: 3642392059; 9783642392054
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-642-39206-1_38

We investigate the approximability of K-Facility Location by deterministic strategyproof mechanisms. Our main result is an elegant characterization of deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location on the line. Specifically, we show that for instances with n ≥ 5 agents, any such mechanism either admits a unique dictator, or always places the facilities at the two extremes. As a consequence, we obtain that the best approximation ratio achievable by deterministic strategyproof mechanisms for 2-Facility Location on the line is precisely n − 2. Employing a technical tool developed for the characterization, we show that for every K ≥ 3, there do not exist any deterministic anonymous strategyproof mechanisms with a bounded approximation ratio for K-Facility Location on the line, even for simple instances with K + 1 agents. Moreover, building on the characterization for the line, we show that there do not exist any deterministic mechanisms with a bounded approximation ratio for 2-Facility Location in more general metric spaces, which is true even for simple instances with 3 agents located in a star.