design strategyproof facility location

This paper studies the multi-agent facility location problem with private agent locations and facility preferences: a single facility must be placed among finitely many candidate locations, and agents may strategically misreport their private information—comprising both locations and preferences—to improve their utility (a function of distance and preference). The objective is to design incentive-compatible mechanisms that approximately maximize social welfare. We first prove that no deterministic mechanism achieves a bounded approximation ratio. We then propose a tight randomized *k*-approximation mechanism. Under the restricted setting where only preferences—not locations—are manipulable, we design an optimal deterministic mechanism with approximation ratio ≈2.325 and establish a matching lower bound of 3/2; for randomized mechanisms in this setting, we derive a tight lower bound of 6/5. Collectively, our work fully characterizes the approximation limits of deterministic and randomized mechanisms in this setting, integrating tools from game-theoretic mechanism design, randomized algorithms, and strategic robustness analysis.

This paper studies the facility location mechanism design problem in metric spaces with learning-augmented predictions, aiming to design strategyproof (SP) mechanisms that minimize the maximum agent cost under truthful reporting, leveraging imperfect predictions. It introduces, for the first time in this setting, the dual desiderata of *consistency*—improved approximation ratio when predictions are accurate—and *robustness*—preservation of the optimal worst-case guarantee regardless of prediction error. The authors propose a deterministic mechanism, MinMaxP. On the real line, MinMaxP achieves a tight (1 + min{1, η})-approximation ratio, where η quantifies prediction error. They extend MinMaxP to two-dimensional ℓₚ spaces and analyze its group-strategyproofness. The theoretical analysis integrates tools from mechanism design and metric geometry, addressing both deterministic and randomized mechanisms. This work establishes the first optimal framework for learning-augmented mechanism design that simultaneously achieves consistency and robustness.

This study addresses the facility location problem under strategic agents whose locations and types—either max-type or sum-type—are private information. The authors design deterministic strategyproof mechanisms for settings where either agent locations or types are partially unknown, and analyze their approximation guarantees. This work presents the first strategyproof solution for facility location problems involving both agent types simultaneously, and quantifies how different forms of information asymmetry affect mechanism performance. When locations are known but types are private, the proposed mechanism achieves a $(3 - 2/k)$-approximation ratio. Improved performance is attainable when only the proportion of each type is known. In the online setting with private locations, a generalized median mechanism yields a 3-approximation.

This study addresses the design of strategyproof mechanisms for dual-facility location on discrete graphs, where heterogeneous agents must be assigned to one of two facilities they approve, with the objective of minimizing the total social distance cost. For line graphs, the authors propose a novel mechanism combining a fixed parity median rule with a strategyproof local covering scheme, achieving the optimal approximation ratio of 4/3 and thereby closing a long-standing theoretical gap. For general connected graphs, they devise a strategyproof 2-approximation mechanism and establish a lower bound of 3/2 on the approximation ratio for the specific case of $K_{1,3}$ (claw) graphs, revealing an inherent computational hardness tied to this graph structure.

This work addresses the two-facility location problem without monetary transfers in metric spaces and proposes a novel randomized strategyproof mechanism that improves the approximation ratio for social cost from 4 to $11/3 \approx 3.667$ over all Ptolemaic metric spaces—including Euclidean spaces—thereby breaking the long-standing 4-approximation barrier for the first time. The mechanism integrates the Proportional mechanism with a newly designed Global Pair mechanism, leveraging their complementary performance on different instance types to achieve a tighter approximation. Additionally, the theoretical lower bound is strengthened from 1.045 to $(1+\sqrt{2})/2 \approx 1.207$. By synthesizing randomized mechanism design, strategyproofness analysis, Ptolemaic space theory, and combinatorial optimization techniques, this study significantly advances the theoretical understanding of the problem.