  A set of vertices $W$ of a graph $G$ is a resolving set if every vertex of
$G$ is uniquely determined by its vector of distances to $W$. In this paper,
the Maker-Breaker resolving game is introduced. The game is played on a graph
$G$ by Resolver and Spoiler who alternately select a vertex of $G$ not yet
chosen. Resolver wins if at some point the vertices chosen by him form a
resolving set of $G$, whereas Spoiler wins if the Resolver cannot form a
resolving set of $G$. The outcome of the game is denoted by $o(G)$ and $R_{\rm
MB}(G)$ (resp. $S_{\rm MB}(G)$) denotes the minimum number of moves of Resolver
(resp. Spoiler) to win when Resolver has the first move. The corresponding
invariants for the game when Spoiler has the first move are denoted by $R'_{\rm
MB}(G)$ and $S'_{\rm MB}(G)$. Invariants $R_{\rm MB}(G)$, $R'_{\rm MB}(G)$,
$S_{\rm MB}(G)$, and $S'_{\rm MB}(G)$ are compared among themselves and with
the metric dimension ${\rm dim}(G)$. A large class of graphs $G$ is constructed
for which $R_{\rm MB}(G) > {\rm dim}(G)$ holds. The effect of twin equivalence
classes and pairing resolving sets on the Maker-Breaker resolving game is
described. As an application $o(G)$, as well as $R_{\rm MB}(G)$ and $R'_{\rm
MB}(G)$ (or $S_{\rm MB}(G)$ and $S'_{\rm MB}(G)$), are determined for several
graph classes, including trees, complete multi-partite graphs, grid graphs, and
torus grid graphs.
