  A pebbling move refers to the act of removing two pebbles from one vertex and
placing one pebble on an adjacent vertex. The goal of graph pebbling is: Given
an initial distribution of pebbles, use pebbling moves to reach a specified
goal vertex called the root. The pebbling number of a graph $\pi(G)$ is the
minimum number of pebbles needed so every distribution of $\pi(G)$ pebbles can
reach every choice of the root. We introduce a new variant of graph pebbling, a
game between two players. One player aims to move a pebble to the root and the
other player aims to prevent this. We show configurations of various classes of
graphs for which each player has a winning strategy. We will characterize the
winning player for a specific class of diameter two graphs.
