Characterization of Strategy-Proof Mechanisms for Two-Facility Location Game on a Line

The paper focuses on characterizing the family of strategy-proof mechanisms for the two-facility location game on a line, where the goal is to place two facilities to serve a group of agents. The authors present a refined characterization of the family of mechanisms with a unique dictator, and reveal several new classes of strategy-proof mechanisms that demonstrate the intricacy of the structure within this family.