Facility Location Games Beyond Single-Peakedness: the Entrance Fee Model

In the one-dimensional facility location problem, agents are located on the real line, and a planner's goal is to build one or more facilities on the line to serve the agents. The cost of an agent is her distance to the nearest facility. The problem asks to locate facilities to minimize the total cost of all agents (the utilitarian objective) or the maximum cost among all agents (the egalitarian objective). It is well-known that both optimization problems can be solved in polynomial time [19]. Over the past decade [1, 3, 7, 21, 23, 27], these problems have undergone intensive study from the perspectives of mechanism design and game theory. A key conversion in the models is that now each agent becomes strategic and may misreport her position to decrease her cost. These new problems are called the facility location games, which require to design mechanisms that elicit the true positions of agents and output facility locations to (approximately) minimize the total or maximum cost. Moulin [22] provides a complete characterization of strategyproof mechanisms for the facility location game on line where agents have single-peaked preferences, with no consideration for the optimization of the objective function.