Mechanism Design without Money for Heterogeneous and Distributed Facility Location Problems

One of the well-established problems in approximate mechanism design without money is the facility location problem. In this context, agents possess private positions along a line, and the goal is to determine the location of a public facility while motivating truthful disclosures and achieving optimal social outcomes.

This presentation presents contributions across three key dimensions of facility location problems: (1) Heterogeneous Two-Facility Location Problem: Addressing a discrete setting where agents occupy nodes on a line graph and possess private preferences for two facilities, the research introduces deterministic strategy-proof mechanisms with improved approximation ratios, surpassing existing approaches. (2) Two-Facility Location with Candidate Positions: Investigating another variant, where agents have private positions and known preferences for two facilities, the study identifies deterministic strategy-proof mechanisms that achieve the best possible approximation ratios for social and maximum costs. (3) Distributed Facility Location Problem: Agents are grouped into districts with positions along a real-number line in setting a distributed facility location. The research analyzes two mechanism classes: unrestricted, where agents directly provide truthful positions, and strategy-proof, designed to incentivize honesty. The study establishes tight bounds for various social objectives, including average social cost, max cost, and other fairness-inspired criteria.

In summary, approximate mechanism design without money addresses complex challenges in multi-agent systems, creating mechanisms that promote truthfulness and optimize societal objectives. This presentation introduces innovative mechanisms and provides comprehensive insights into facility location problems from three distinct perspectives.