Mechanism Design with Predictions for Facility Location Games with Candidate Locations

We study mechanism design with predictions in the single (obnoxious) facility location games with candidate locations on the real line, which complements the existing literature on mechanism design with predictions. We first consider the single facility location games with candidate locations, where each agent prefers the facility (e.g., a school) to be located as close to her as possible. We study two social objectives: minimizing the maximum cost and the social cost, and provide deterministic, anonymous, and group strategy-proof mechanisms with predictions that achieve the best possible trade-offs between consistency and robustness, respectively. Additionally, we represent the approximation ratio as a function of the prediction error, indicating that mechanisms can achieve better performance even when predictions are not fully accurate. We also consider the single obnoxious facility location games with candidate locations, where each agent prefers the facility (e.g., a garbage transfer station) to be located as far away from her as possible. For the objective of maximizing the minimum utility, we prove that any strategy-proof mechanism with predictions is unbounded robust. For the objective of maximizing the social utility, we provide a deterministic, anonymous, and group strategy-proof mechanism with prediction that achieves the best possible trade-off between consistency and robustness.