Two-facility Location Games with Minimum Distance Requirement

We study the mechanism design problem of a social planner for locating two facilities on line interval [0, 1], where set n strategic agents report their locations and determines facilities. consider requirement minimum distance 0 ≤ d 1 between Given are heterogeneous, we model cost/utility an agent as sum his distances to both In heterogeneous two-facility location game minimize cost, show that optimal solution can be computed in polynomial time prove carefully choosing one output is strategyproof. also strategyproof minimizing maximum cost. homogeneous, closer facility. homogeneous any deterministic has unbounded approximation ratio. Moreover, obnoxious maximizing utility, propose new group mechanisms with provable ratios establish lower bound (7 − d)/6 mechanism. utility. 4/3. Besides, triple-preference, each facility may favorable, obnoxious, indifferent agent, further motivate preferences towards truthfully, ratio 4.