# Nash Welfare and Facility Location

arXiv: https://arxiv.org/abs/2310.04102 · HTML: https://mlsanity.com/paper/2310.04102/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 39 references that are in the map.
- First posted on arXiv 6 Oct 2023.

## Builds on (most cited first, 6 of 6)

- [Fair mixing: the case of dichotomous preferences](https://mlsanity.com/paper/1712.02542/) (2017)
- [On Voting and Facility Location](https://mlsanity.com/paper/1512.05868/) (2015)
- [Facility Location Problem with Capacity Constraints: Algorithmic and Mechanism Design Perspectives](https://mlsanity.com/paper/1911.09813/) (2019)
- [The Capacity Constrained Facility Location problem](https://mlsanity.com/paper/1806.00960/) (2018)
- [Strategy-Proof Facility Location for Concave Cost Functions](https://mlsanity.com/paper/1305.3333/) (2013)
- [Strategy Proof Mechanisms for Facility Location in Euclidean and Manhattan Space](https://mlsanity.com/paper/2009.07983/) (2020)

## Built on by (most cited first, 1 of 1)

- [Equitable Mechanism Design for Facility Location](https://mlsanity.com/paper/2506.10460/) (2025)

## Abstract (arXiv)

We consider the problem of locating a facility to serve a set of agents located along a line. The Nash welfare objective function, defined as the product of the agents' utilities, is known to provide a compromise between fairness and efficiency in resource allocation problems. We apply this welfare notion to the facility location problem, converting individual costs to utilities and analyzing the facility placement that maximizes the Nash welfare. We give a polynomial-time approximation algorithm to compute this facility location, and prove results suggesting that it achieves a good balance of fairness and efficiency. Finally, we take a mechanism design perspective and propose a strategy-proof mechanism with a bounded approximation ratio for Nash welfare.