# From Hotelling to Load Balancing: Approximation and the Principle of Minimum Differentiation

arXiv: https://arxiv.org/abs/1903.04265 · HTML: https://mlsanity.com/paper/1903.04265/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2019.

## Built on by (most cited first, 4 of 4)

- [Two-Stage Facility Location Games with Strategic Clients and Facilities](https://mlsanity.com/paper/2105.01425/) (2021)
- [Strategic Facility Location with Clients that Minimize Total Waiting Time](https://mlsanity.com/paper/2211.14016/) (2022)
- [Equilibria in Two-Stage Facility Location with Atomic Clients](https://mlsanity.com/paper/2403.03114/) (2024)
- [The Bakers and Millers Game with Restricted Locations](https://mlsanity.com/paper/2501.05334/) (2025)

## Abstract (arXiv)

Competing firms tend to select similar locations for their stores. This phenomenon, called the principle of minimum differentiation, was captured by Hotelling with a landmark model of spatial competition but is still the object of an ongoing scientific debate. Although consistently observed in practice, many more realistic variants of Hotelling's model fail to support minimum differentiation or do not have pure equilibria at all. In particular, it was recently proven for a generalized model which incorporates negative network externalities and which contains Hotelling's model and classical selfish load balancing as special cases, that the unique equilibria do not adhere to minimum differentiation. Furthermore, it was shown that for a significant parameter range pure equilibria do not exist. We derive a sharp contrast to these previous results by investigating Hotelling's model with negative network externalities from an entirely new angle: approximate pure subgame perfect equilibria. This approach allows us to prove analytically and via agent-based simulations that approximate equilibria having good approximation guarantees and that adhere to minimum differentiation exist for the full parameter range of the model. Moreover, we show that the obtained approximate equilibria have high social welfare.