Strategyproof Facility Location with Concave Costs

In k-Facility Location games, n strategic agents report their locations on the real line and a mechanism maps them to k facilities. Each agent seeks to minimize her connection cost to the nearest facility and the mechanism should be strategyproof and approximately efficient. Facility Location games have received considerable attention in the framework of approximate mechanism design without money. In this letter, we discuss some recent positive results on the approximability of k-Facility Location by randomized strategyproof mechanisms. Interestingly, these results hold even if the agents' connection cost is a concave cost function of the distance. Categories and Subject Descriptors: F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity; J.4 [Computer Applications]: Social and Behavioral Sciences Economics