Equitable Mechanism Design for Facility Location
This addresses fairness in resource allocation for agents in facility location problems, but is incremental as it builds on existing literature with new impossibility results and approximation analyses.
The paper tackles the problem of designing strategy-proof mechanisms for facility location that maximize equitability, measured by the Gini index, and proves an impossibility result for approximating the optimal Gini index, then proposes analyzing approximation ratios for the complemented Gini index and Nash welfare.
We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility result that no strategy proof mechanism can bound the approximation ratio of the optimal Gini index of utilities for one or more facilities. We propose instead computing approximation ratios of the complemented Gini index of utilities, and consider how well both deterministic and randomized mechanisms approximate this. In addition, as Nash welfare is often put forwards as an equitable compromise between egalitarian and utilitarian outcomes, we consider how well mechanisms approximate the Nash welfare.