[KolenCh]

Photon-photon interaction is photon self interaction. Gravity/graviton self interaction then means graviton-graviton interaction. In general relativity, all form of energy would have an effect of gravity, and also react to gravity. Since all matter, including photon and graviton, has energy, then they should self interact.

In QED, photon and photon do interacts too and you can calculate its effect to be small. In GR, you can expect self interaction is small if the space time curvature is small.

(Photon is the particle that mediates QED, and graviton is the hypothetical particle that mediates gravity.)