Optimal Group Manipulation in Facility Location Problems

We address optimal group manipulation in multidimensional, multi-facility location problems. We focus on two families of mechanisms, generalized median and quantile mechanisms, evaluating the difficulty of group manipulation of these mechanisms. We show that, in the case of single-facility problems, optimal group manipulation can be formulated as a linear or second-order cone program, under the L1and L2-norms, respectively, and hence can be solved in polynomial time. For multiple facilities, we show that optimal manipulation is NP-hard, but can be formulated as a mixed integer linear or second-order cone program, under the L1and L2-norms, respectively. Despite this hardness result, empirical evaluation shows that multi-facility manipulation can be computed in reasonable time with our formulations.