New Envy Ratio Metric Optimizes Fair Facility Location Mechanisms
A game-theoretic fairness metric yields optimal strategyproof facility placement algorithms.
A team led by Yuan Ding and Wenjing Liu has introduced a new fairness metric—the envy ratio—to the facility location game on a line. The envy ratio captures egalitarianism by considering the maximum ratio between any two agents' utilities. The researchers investigate both deterministic and randomized mechanisms that are strategyproof (or group strategyproof) and minimize this objective.
In the first setting, all agents and the facility are confined to a fixed interval. They produce an optimal deterministic mechanism that is also group strategyproof, and provide a lower bound for randomized mechanisms. The second setting allows agents anywhere on the real line but restricts the facility to a relative interval. Here, they present lower bounds and two upper bounds for randomized strategyproof mechanisms. These results offer practical insights for fair resource allocation in AI systems, such as placing public amenities or servers to minimize envy among users.
- Introduces envy ratio as a new objective for facility location games, measuring maximum utility ratio between agents.
- Provides optimal deterministic strategyproof (and group strategyproof) mechanisms for both interval-restricted and relative-interval settings.
- Gives lower bounds for randomized mechanisms, establishing fundamental limits on fairness under strategyproofness.
Why It Matters
Fair facility placement directly impacts AI systems managing shared resources, from cloud servers to urban logistics.