On (Group) Strategy-Proof Mechanisms without Payment for Facility Location Games

We characterize the performance of strategy proof and group-strategy proof social choice rules, for placing a facility on the nodes of a metric network inhabited by N autonomous self-interested agents. Every agent owns a set of locations and caters to minimization of its cost which is the total distance from the facility to its locations. Agents may misreport their locations, so as to manipulate the outcome. A central authority has a set of allowable locations where the facility could be opened. The authority must devise a mechanism that, given the agents reports, places the facility in an allowable location that minimizes the utilitarian social cost - the sum of agents costs. A mechanism is strategyproof (SP) if no agent may misreport its locations and be better off; it is group-strategyproof (GSP) if no coalition of agents benefits by jointly misreporting their locations The requirement for (G)SP in this setting makes optimum placement of the facility impossible and, therefore, we consider approximation (G)SP mechanisms. For SP mechanisms, we give a simple 3-approximation randomized mechanism and also provide asymptotic lower bounds for different variants. For GSP mechanisms, a (2N+1)-approximation deterministic GSP mechanism is devised. Although the mechanism is simple, we showed that it is asymptotically optimal up to a constant. Our Omega(N1-epsilon) lower bound that randomization cannot improve over the approximation factor achieved by the deterministic mechanism, when GSP is required.