We present a fully microscopic approach to the transition rate of two exciton-photon polaritons. The non-trivial consequences of the polariton composite nature-here treated exactly through a development of our composite-exciton many-body theory-lead to results noticeably different from the ones of the conventional approaches in which polaritons are mapped into elementary bosons. Our work reveals an appealing fundamental scattering which corresponds to a photon-assisted exchange -in the absence of Coulomb process. This scattering being dominant when one of the scattered polaritons has a strong photon character, it should be directly accessible to experiment. In the case of microcavity polaritons, it produces a significant enhancement of the polariton transition rate when compared to the one coming from Coulomb interaction. This paper also contains the crucial tools to securely tackle the many-body physics of polaritons, in particular towards its possible BEC. Copyright (c) EPLA, 2007.