  The mean field equation involving the $N$-Laplace operator and an exponential
nonlinearity is considered in dimension $N\geq2$ on bounded domains with
homogenoeus Dirichlet boundary condition. By a detailed asymptotic analysis we
derive a quantization property in the non-compact case, yielding to the
compactness of the solutions set in the so-called non-resonant regime. In such
a regime, an existence result is then provided by a variational approach.
