that is very sensitive to faults and ask how would the players adapt their strategies in a given fault model.

#### Organization.

The paper is organized as follows. Section \[sec:model\] presents the Hotelling game formally along with known results. Sections \[sec:disconnect\] and \[sec:crash\] analyze the Hotelling game with line disconnections and server crashes, respectively. Section \[sec:conclusion\] concludes the paper and offers future directions of research.

Model and Preliminaries {#sec:model}
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#### The Game.

The Hotelling game on the line segment $[a,b]$, denoted as $H(n,[a,b])$, involves $n$ servers, $s_i$ for $i=1,\ldots,n$, who place themselves at different points $\loc_i$ on the segment. Each point on the line also represents a client, who will be served by the nearest server. The *market* of each server is the line segment containing the clients that will be served by it (this segment is also known as the server’s *Voronoi cell*). The payoff of each server $s_i$, denoted $p(s_i)$, is the length of his market. Servers strive to maximize their payoff.

We assume clients are uniformly distributed over the line. We also assume that no more than one server can occupy a given location; the minimal distance between two servers is some arbitrarily small $\varepsilon>0$.[^3] When 