---
abstract: 'The $n$-player Hotelling game calls for each player to choose a point on the line segment, so as to maximize the size of his Voronoi cell. This paper studies fault-tolerant versions of the Hotelling game. Two fault models are studied. The first studied: line faults and player faults. The first model assumes that the environment is prone to failure: with some probability, a disconnection occurs at a random point on the line, splitting it into two separate segments and modifying each player’s Voronoi cell accordingly. A complete characterization of the Nash equilibria of this variant is provided for every $n$. Additionally, a one to one correspondence is shown between equilibria of this variant and of the Hotelling game with no faults. The second fault model assumes the players are prone to failure: each player is removed from the game with probability, changing the payoffs of the remaining players accordingly. It is shown that for $n \geq 3$ this variant of the game has no Nash equilibria.'
author:
- Chen Avin
- Avi Cohen
- Zvi Lotker
- David Peleg
- 'Chen Avin[^1]'
- 'Avi Cohen[^2]'
- 'Zvi Lotker$^*$'
- 'David Peleg$^{\dag}$'
title: 'Fault-Tolerant Hotelling Games'
---

Introduction
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