  The main topic of this paper is motivated by a localization problem in
cellular networks. Given a graph $G$ we want to localize a walking agent by
checking his distance to as few vertices as possible. The model we introduce is
based on a pursuit graph game that resembles the famous Cops and Robbers game.
It can be considered as a game theoretic variant of the \emph{metric dimension}
of a graph. We provide upper bounds on the related graph invariant $\zeta (G)$,
defined as the least number of cops needed to localize the robber on a graph
$G$, for several classes of graphs (trees, bipartite graphs, etc). Our main
result is that, surprisingly, there exists planar graphs of treewidth $2$ and
unbounded $\zeta (G)$. On a positive side, we prove that $\zeta (G)$ is bounded
by the pathwidth of $G$. We then show that the algorithmic problem of
determining $\zeta (G)$ is NP-hard in graphs with diameter at most $2$.
Finally, we show that at most one cop can approximate (arbitrary close) the
location of the robber in the Euclidean plane.
