Fault-Tolerant Hotelling Games

TL;DR

This paper explores fault-tolerant versions of the Hotelling game, analyzing how line and player failures affect Nash equilibria and establishing new theoretical insights into these modified strategic interactions.

Contribution

It provides a complete characterization of Nash equilibria under line faults and shows the absence of equilibria when players are prone to failure for three or more players.

Findings

Line faults alter the structure of Nash equilibria.

A one-to-one correspondence exists between fault-tolerant and standard Hotelling equilibria.

No Nash equilibria exist when players can fail with probability for three or more players.

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: 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 i.i.d. 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.