On the Power of Deterministic Mechanisms for Facility Location Games
Dimitris Fotakis, Christos Tzamos

TL;DR
This paper characterizes deterministic strategyproof mechanisms for 2-Facility Location on the line, revealing their limitations and uniqueness, and extends the analysis to general metric spaces, showing broader impossibility results.
Contribution
It provides a complete characterization of deterministic strategyproof mechanisms for 2-Facility Location on the line, and proves the non-existence of such mechanisms with bounded approximation ratios for larger K and general metric spaces.
Findings
Deterministic strategyproof mechanisms for 2-Facility Location on the line are either dictators or place facilities at extremes.
The Two-Extremes mechanism is uniquely anonymous and strategyproof with a bounded approximation ratio.
No deterministic anonymous strategyproof mechanisms with bounded approximation ratios exist for K-Facility Location with K ≥ 3 or in general metric spaces.
Abstract
We consider K-Facility Location games, where n strategic agents report their locations in a metric space, and a mechanism maps them to K facilities. Our main result is an elegant characterization of deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location on the line. In particular, we show that for instances with n \geq 5 agents, any such mechanism either admits a unique dictator, or always places the facilities at the leftmost and the rightmost location of the instance. As a corollary, we obtain that the best approximation ratio achievable by deterministic strategyproof mechanisms for the problem of locating 2 facilities on the line to minimize the total connection cost is precisely n-2. Another rather surprising consequence is that the Two-Extremes mechanism of (Procaccia and Tennenholtz, EC 2009) is the only deterministic anonymous…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGame Theory and Voting Systems · Auction Theory and Applications · Optimization and Search Problems
