The question itself is pretty self explanatory. I asked this to my chemistry teacher when he was doing the photoelectric effect while teaching atomic structure, and he just shrugged it off.
One possible mechanism that I thought up, is an atom with a unpaired electron (say hydrogen) to absorb one photon, and jump to a higher energy level, and then just immediately be hit by another photon with a different energy which raises it to an even higher level. Then finally the electron falls back into its proper non exited state releasing not two but only one photon which has the energy of both the initial photons, ideally combining photons.
Is this mechanism correct? Does it occur in nature? Do photons have other ways in which they merge? or do they not merge at all?