  We study the graph energy from a cooperative game viewpoint. We introduce
\emph{the graph energy game} and show various properties. In particular, we see
that it is a superadditive game and that the energy of a vertex, as defined in
Arizmendi and Juarez-Romero (2018), belongs to the core of the game. These
properties imply new bounds for the energy of graphs. We also consider a
version based on $p$-Schatten norms.
