  Strategic games admit a multi-graph representation, in which two kinds of
relations, accessibility, and preferences, are used to describe how the players
compare the possible outcomes. A category of games with a fixed set of players
$\mathbf{Gam}_I$ is built from this representation, and a more general category
$\mathbf{Gam}$ is defined with games having different sets of players, both
being complete and cocomplete. The notion of Nash equilibrium can be
generalized in this context. We then introduce two subcategories of
$\mathbf{Gam}$, $\mathbf{NE}$ and $\mathbf{Gam}^{NE}$ in which the morphisms
are equilibria-preserving. We illustrate the expressivity and usefulness of
this framework with some examples.
