  We study $p$-energies on post critically finite (p.c.f.) self-similar sets
for $1<p<\infty$, as limits of discrete $p$-energies on approximation graphs,
extending the construction of Dirichlet forms, the $p=2$ setting. By suitably
enlarging the choices of discrete $p$-energies, and employing the energy
averaging method developed by Kusuoka-Zhou, we prove the existence of symmetric
$p$-energies on affine nested fractals, and extend Sabot's celebrated criterion
for existence and non-existence of Dirichlet forms on p.c.f. self-similar sets
to the $1<p<\infty$ setting.
