Approximate Strategyproof Mechanisms for Facility Location Games

22^nd January 2013, 16:00 Ashton Lecture Theatre
Dr. Dimitris Fotakis
Division of Computer Science
NTUA Athens
Greece

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. The agents seek to minimize their connection cost, namely the distance of their true location to the nearest facility, and may misreport their location. We are interested in (deterministic or randomized) mechanisms that are strategyproof, i.e., ensure that no agent can benefit from misreporting her location, do not resort to monetary transfers, and achieve a good approximation ratio to either the total connection cost or the maximum connection cost of the agents.

We present 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 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.

Building on the techniques used for the characterization, we also show that:

-- For every k \geq 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.

-- There do not exist any deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location on general metric spaces, which is true even for simple instances with 3 agents located in a star.

On the positive side, we present a randomized mechanism for locating k facilities on the line that achieves an approximation ratio of 2 for the objective of maximum cost.