day to day life, uncertainly must be accounted for. For instance, one of the players may fail to open their store due to illness or vacation, or the road might be blocked due to infrastructure work or safety issues, denying clients access to their preferred vendor. While it is uncertain whether such an event occurs on a given day or not, it is certain to happen one day. It therefore stands to reason that failures would be accounted for in player strategies and payoffs. Indeed, fault-tolerant problems constitute a fertile area of research in Computer Science. Yet, to the best of our knowledge, this paper is the first to consider fault-tolerance aspects of the Hotelling game.

#### Contributions.

We analyzed two types of failure models. In the first variant, we consider a failure prone *environment*, wherein it is possible that the line would be blocked at a random point, denying the passage of clients through it. We refer to this variant of the game with $n$ players as the [*Line Failure Hotelling game*]{} and denote it by $H_{{\mbox{\small \sc lf}}}(n)$. We characterize all existing equilibria of $H_{{\mbox{\small \sc lf}}}(n)$ (Theorem \[thm:disconnect\]). Moreover, we show that each Nash equilibrium of $H_{{\mbox{\small 