$\loc_1=\loc_2=1/4$, and the other two at $\loc_3=\loc_4=3/4$. *Five Servers.* There is a unique equilibrium, where two servers are paired at $\loc_1=\loc_2=1/6$, two others are paired at $\loc_4=\loc_5=5/6$, and an isolated server is located at $\loc_3=1/2$. Note that here, the payoffs are not uniform: $s_3$ has payoff $p(s_3)=1/3$, while all other servers have payoff $1/6$.

*More than five Servers.* There exist infinitely many equilibria, characterized as follows: peripheral servers are paired with their neighbors and have identical hinterlands. Each peripheral pair is separated from the closest server by a distance twice as long as the hinterland. The interior servers are paired or isolated.

As an example, consider the game $H(6,[0,1])$. Let the length of the hinterland be $x$, and without loss of generality let the servers be ordered such that $ \loc_1 < \loc_2 < \ldots < \loc_6 $. From the above characterization of equilibria, it follows that in every equilibrium $s_1$ and $s_2$ are paired at $\loc_1=\loc_2=x$, $s_3$ is located at $\loc_3=3x$, $s_4$ is located at $\loc_4=1-3x$ and $s_5$ and $s_6$ are paired at $\loc_5=\loc_6=1-x$. The distance between $s_3$ and $s_4$ is at least $\varepsilon$ and at most $2x$ (by condition \[p2\]).

That is, the above described configuration is an 