Facility Location with Entrance Fees

In mechanism design, the facility location game is an extensively studied problem. In the classical model, the cost of each agent is her distance to the nearest facility. In this paper, we consider a new model, where there is a location-dependent entrance fee to the facility. Thus, in our model, the cost of each agent is the sum of the distance to the facility and the entrance fee of the facility. This is a refined generalization of the classical model. We study the model and design strategyproof mechanisms. For one and two facilities, we provide upper and lower bounds for the approximation ratio given by deterministic and randomized mechanisms, with respect to the utilitarian objective and the egalitarian objective. Most of our bounds are tight and these bounds are independent of the entrance fee functions. Our results are as general as possible because the entrance fee function we consider is arbitrary.