We characterize the performance of strategyproof and group-strategyproof 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
Ω(N1 - ε)
lower bound that randomization cannot improve over the approximation factor achieved
by the deterministic mechanism, when GSP is required.