# Hotelling-Downs Model with Limited Attraction

arXiv: https://arxiv.org/abs/1611.05959 · HTML: https://mlsanity.com/paper/1611.05959/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2016.

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

- [How Bad is Top-K Recommendation under Competing Content Creators?](https://mlsanity.com/paper/2302.01971/) (2023)
- [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)

## Abstract (arXiv)

In this paper we study variations of the standard Hotelling-Downs model of spatial competition, where each agent attracts the clients in a restricted neighborhood, each client randomly picks one attractive agent for service. Two utility functions for agents are considered: support utility and winner utility. We generalize the results by Feldman et al. to the case where the clients are distributed arbitrarily. In the support utility setting, we show that a pure Nash equilibrium always exists by formulating the game as a potential game. In the winner utility setting, we show that there exists a Nash equilibrium in two cases: when there are at most 3 agents and when the size of attraction area is at least half of the entire space. We also consider the price of anarchy and the fairness of equilibria and give tight bounds on these criteria.