= Solution
\b[There is no pure <Nash equilibrium>.] If the firms choose different sites, $S$ serves at least its own building, so $C$ receives less than $2k$. By moving onto $S$'s site, $C$ makes every customer equidistant from the two shops and wins every tie, obtaining $2k$. Thus any separated profile has a profitable <unilateral deviation> by $C$.
At any co-located profile, $S$ receives zero. It can move to a different site and capture at least that site's customers, obtaining at least two. Thus every co-located profile also has a profitable <unilateral deviation>. These cases exhaust all pure <strategy profiles>.
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